Polar encoding and decoding method and apparatus for satellite communication

An apparatus for encoding polar code, comprising:

• a processor, and
• a memory coupled to the processor to store instructions, which when executed by the processor, cause the apparatus to:
• obtain K bits to be encoded;
• select K sequence numbers from a first sequence, wherein the K bits are placed on polar channels corresponding to the K sequence numbers;
• perform polar code encoding on the K bits to obtain encoded bits, wherein the first sequence comprises sequence numbers of N polar channels, the first sequence is one of Q1, Q2, a sub-sequence Q1 or a sub-sequence Q2, K is a positive integer, N is a mother code length of polar code, N=2n, n is a positive integer, and K≤N;
• transmit a signal comprising the encoded data bits,
• wherein sequence Q1=[0,1,2,4,8,16,3,32,5,6,9,64,10,17,12,18,128,33,20,34,7,24,36,65,11,256,66,40,13,19,68,14,129,4 8,21,72,130,35,22,25,512,132,37,80,26,38,257,67,136,41,28,258,96,69,42,15,144,49,260,70,44,7 3,131,50,23,1024,264,74,160,513,133,52,81,27,76,514,134,39,272,82,137,56,29,516,259,192,97, 138,84,43,30,145,288,98,261,71,520,140,45,88,146,51,262,100,1025,46,265,75,2048,161,528,14 8,53,320,1026,266,104,77,162,515,135,54,273,83,152,57,1028,268,78,544,164,517,274,193,112, 139,85,58,31,1032,518,384,289,194,99,276,168,86,521,141,60,89,147,290,576,263,196,101,522, 142,1040,47,280,90,2049,176,529,149,292,102,321,1027,524,267,200,105,2050,92,163,530,150, 55,322,1056,153,296,1029,106,269,79,640,545,2052,165,532,275,208,113,154,324,59,1030,270, 108,546,1033,166,519,385,304,195,114,2056,277,169,87,536,156,61,1088,328,1034,548,386,29 1,224,577,278,197,170,116,523,143,1041,62,281,91,2064,177,1036,768,578,388,293,198,103,55 2,336,172,1042,525,282,201,120,2051,93,178,531,151,294,580,323,1152,1057,526,392,297,202, 1044,107,284,2080,94,641,560,2053,180,533,209,352,1058,155,325,298,1031,584,271,204,109, 642,547,2054,1048,167,534,400,305,210,115,2057,184,326,537,1060,157,300,1089,110,329,103 5,644,549,387,2112,306,225,592,2058,279,212,171,117,538,158,1280,63,1090,330,1064,2065,5 50,416,1037,769,226,579,389,308,199,648,118,553,2060,337,173,1043,540,283,216,121,1092,2 066,332,179,1038,770,608,390,295,228,581,554,338,1153,174,1072,527,393,312,203,1045,122, 2176,285,2081,95,656,561,2068,181,1096,772,582,448,353,1154,1059,556,394,340,299,232,104 6,585,286,205,2082,124,643,562,2055,1049,182,535,401,211,354,2072,1536,185,327,1156,776, 1061,586,396,301,206,1104,111,672,344,2084,1050,645,564,402,2113,307,240,593,2059,213,18 6,356,539,1062,159,1281,302,1091,588,331,1160,1065,646,2304,551,417,2114,1052,784,227,59 4,404,2088,309,214,649,119,568,2061,188,1282,541,1120,217,360,1093,1066,2067,333,418,103 9,771,704,609,391,2116,310,229,650,596,555,2062,339,1168,175,1073,542,408,313,218,1284,1 23,1094,2177,2096,334,657,1068,800,2069,610,420,1097,773,230,583,449,368,1155,652,1074,5 57,395,2120,341,314,233,1047,600,2178,287,220,2083,125,658,563,2070,1288,183,1098,774,61 2,450,355,1184,2073,1537,558,424,342,1157,777,234,1076,587,397,316,207,2560,1105,126,673, 2180,345,2085,1051,660,565,403,2128,241,1100,832,2074,1538,452,187,357,1158,778,1063,61 6,398,1296,303,236,1106,589,674,346,1161,2086,1080,647,2305,566,432,2115,1053,785,242,21 84,595,405,2089,215,664,358,569,2076,1540,189,1283,1216,780,1121,590,456,361,1162,1108,1 067,676,2306,348,419,2144,1054,786,705,624,406,2117,2090,311,244,651,597,570,2063,1169,1 90,1312,543,409,1122,219,1285,362,1095,2192,1544,2097,335,1164,896,1069,801,706,2308,61 1,421,2118,1112,788,231,680,598,464,2092,369,1170,653,1075,572,410,2121,315,248,1286,601, 1124,2179,221,2098,364,659,1070,802,2071,1289,422,1099,775,708,613,451,3072,370,1185,65 4,2312,1552,559,425,2122,343,1172,792,235,1077,602,412,2208,317,222,2561,1344,127,688,21 81,2100,1290,661,1128,804,2129,614,480,1101,833,1186,2075,1539,453,426,372,1159,779,712, 1078,617,399,2124,1297,318,237,2562,1107,604,675,2182,347,1176,2087,1081,662,2320,567,4 33,2130,1292,243,1102,2185,834,2104,1568,454,665,359,1188,808,2077,1541,618,428,1298,12 17,781,238,1136,591,457,376,1163,2564,1109,1082,677,2307,2240,349,434,2145,1055,787,720, 2186,625,407,2132,2091,245,666,836,571,2078,1542,1408,191,1313,1218,782,1123,620,458,13 00,363,1192,1110,2193,1545,678,2336,350,1165,897,2146,1084,816,707,2309,626,436,2119,25 68,1113,789,246,681,2188,599,465,2093,1171,668,1314,573,411,2136,1600,249,1287,1220,840, 1125,2194,1546,460,2099,365,1166,898,1071,803,736,2310,1304,423,2148,1114,790,709,682,6 28,466,3073,2094,371,1200,655,2313,1553,574,440,2123,1173,793,250,1316,603,413,1126,220 9,223,2576,1345,366,689,2196,1548,2101,1291,1224,900,1129,805,710,2368,615,481,3074,111 6,848,1187,684,2314,1554,468,427,2152,373,1174,794,713,1079,632,414,2125,2210,319,252,25 63,1346,605,690,2183,1177,2102,1320,663,2321,1130,806,2131,1293,482,1103,2200,835,1664, 2105,1569,455,3076,904,374,1189,809,714,2316,1556,619,429,2126,1299,1232,796,239,2592,1 137,606,472,2212,377,1178,2565,1348,1083,692,2322,2241,435,2160,1294,721,1132,2187,864, 2133,2106,1570,484,667,837,1190,810,2079,1543,1409,430,1328,1219,783,716,1138,621,459,3 080,1301,378,1193,2566,1111,2432,1560,679,2337,2242,351,1180,912,2147,1085,817,722,2324, 2216,627,437,2134,2569,1352,247,696,2189,838,2108,1572,1410,669,1315,1248,812,2137,160 1,622,488,1302,1221,841,1194,1140,2195,1547,461,2338,380,1167,899,2624,1086,818,737,231 1,2244,1305,438,2149,2570,1115,791,724,683,2190,629,467,3088,2095,1201,670,2328,1792,57 5,441,2138,1602,1412,251,1317,1222,842,1127,2224,1576,462,2577,1360,367,1196,928,2197,1 549,738,2340,1306,1225,901,2150,1144,820,711,2369,630,496,3075,2572,1117,849,1202,685,2 315,2248,1555,469,442,2153,1175,795,728,1318,633,415,2140,1604,2211,253,2578,1347,844,6 91,2198,1550,1416,2103,1321,1226,902,1131,807,740,2370,1308,483,3104,1118,2201,850,1665, 686,2344,1584,470,3077,905,2154,375,1204,824,715,2317,1557,634,444,2127,2688,1233,797,2 54,2593,1376,607,473,2213,1179,2580,1349,1322,693,2323,2256,1608,2161,1295,1228,960,113 3,2202,865,1666,2372,2107,1571,485,3078,906,852,1191,811,744,2318,1558,1424,431,2156,13 29,1234,798,717,2594,1139,636,474,3081,2214,379,1208,2567,1350,2433,1561,694,2352,2243, 1181,913,2162,1324,723,2325,1134,2217,866,2135,2584,1353,486,697,2204,839,1668,2109,157 3,1411,3136,908,1330,1249,813,718,2376,1616,623,489,3082,1303,1236,856,1195,2596,1141,2 434,1562,476,2339,2272,381,1182,914,2625,1087,819,752,2326,2245,2218,439,2164,2571,1354, 725,698,2191,868,3089,2110,1574,1440,671,2329,1793,1250,814,2139,1603,1413,490,1332,12 23,843,1672,1142,2225,1577,463,3084,2816,1361,382,1197,929,2626,2436,1564,739,2341,2246, 1307,1240,916,2151,2600,1145,821,726,2384,2220,631,497,3090,2573,1356,1203,700,2330,22 49,1794,443,2168,1632,1414,729,1319,1252,872,2141,1605,2226,1578,492,2579,1362,845,1198, 930,2199,1551,1417,2342,1336,1227,903,2628,1146,822,741,2371,3200,1309,498,3105,2574,1 119,2440,851,1680,687,2345,2250,1585,471,3092,920,2155,1205,825,730,2332,1796,635,445,2 142,1606,2689,1472,255,2608,1377,846,2228,1580,1418,2581,1364,1323,1256,932,2257,1609,7 42,2400,1310,1229,961,3106,1148,2203,880,1667,2373,2346,1586,500,3079,907,2632,853,1206, 826,745,2319,2252,1559,1425,446,2157,2690,1235,799,732,2595,1378,637,475,3096,2215,120 9,2582,1351,2448,1800,695,2353,2258,1610,1420,2163,1325,1230,962,1135,2232,867,1696,237 4,2585,1368,487,3108,936,2205,854,1669,746,2348,1588,1426,3137,909,2158,1331,1264,828,7 19,2377,1617,638,504,3083,2692,1237,857,1210,2597,1380,2435,1563,477,2354,2273,1183,915, 2640,1326,753,2327,2260,1612,2219,2165,2586,1355,964,699,2206,869,1670,3328,2111,1575, 1441,3138,910,1808,1251,815,748,2378,1618,1428,491,3112,1333,1238,858,1673,2598,1143,24 64,1592,478,3085,2817,2274,383,1212,944,2627,2437,1565,754,2356,2247,2696,1241,917,2166, 2601,1384,727,2385,2221,870,3091,2588,1357,1442,701,2331,2264,1795,1728,2169,1633,1415, 3140,968,1334,1253,873,1674,2380,1620,2227,1579,493,3086,2818,1363,860,1199,931,2656,2 438,1566,1432,2343,2276,1337,1242,918,2629,2602,1147,823,756,2386,3201,2222,499,3120,25 75,1358,2441,1681,702,2360,2251,1824,3093,921,2170,1634,1444,731,2333,1797,1254,874,214 3,1607,2704,1473,494,2609,1392,847,1676,2229,1581,1419,3144,2820,1365,1338,1257,933,263 0,2496,1624,743,2401,3202,1311,1244,976,3107,2604,1149,2442,881,1682,2388,2347,2280,158 7,501,3094,922,2633,1207,827,760,2334,2253,1798,447,2172,1636,2691,1474,733,2610,1379,8 76,3097,2230,1582,1448,2583,1366,2449,1801,1258,934,2259,1611,1421,2402,1340,1231,963,3 584,1150,2233,882,1697,2375,3204,2824,1369,502,3109,937,2634,2444,855,1684,747,2349,225 4,1589,1427,3152,924,2159,2720,1265,829,734,2392,1856,639,505,3098,2693,1476,1211,2612, 1381,2450,1802,2355,2288,1640,1422,2641,1327,1260,992,2261,1613,2234,1698,2404,2587,13 70,965,3110,938,2207,884,1671,3329,2350,1590,1456,3139,911,2636,1809,1266,830,749,2379, 3208,1619,1429,506,3113,2694,1239,859,1688,2599,1382,2465,1593,479,3100,2832,2275,1213, 945,2642,2452,1804,755,2357,2262,1614,2697,1480,2167,2616,1385,966,2236,871,1700,3330,2 589,1372,1443,3168,940,2265,1810,1729,750,2408,1648,1430,3141,969,3114,1335,1268,888,16 75,2381,1621,2466,1594,508,3087,2819,2752,861,1214,946,2657,2439,1567,1433,2358,2277,26 98,1243,919,2644,2603,1386,757,2387,3216,2223,3121,2590,1359,2456,1920,703,2361,2266,18 25,1730,3332,2171,1635,1445,3142,970,1812,1255,875,1704,2382,1622,2705,1488,495,3116,28 48,1393,862,1677,2658,2468,1596,1434,3145,2821,2278,1339,1272,948,2631,2497,1625,758,24 16,3203,2700,1245,977,3122,2605,1388,2443,1683,2389,2362,2281,1826,3095,923,2648,1446,7 61,2335,2268,1799,1732,2173,1637,2706,1475,972,2611,1394,877,1678,3336,2231,1583,1449,3 146,2822,1367,1816,1259,935,2660,2498,1626,1436,2403,3232,1341,1246,978,3585,2606,1151, 2472,883,1712,2390,3205,2825,2282,503,3124,952,2635,2445,1685,762,2364,2255,1828,3153,9 25,2174,1638,2721,1504,735,2393,1857,878,3099,2708,1477,1450,2613,1396,2451,1803,1736,2 289,1641,1423,3148,2880,1342,1261,993,3586,2500,1628,2235,1699,2405,3206,2826,1371,980, 3111,939,2664,2446,885,1686,3344,2351,2284,1591,1457,3154,926,2637,2722,1267,831,764,23 94,3209,1858,507,3128,2695,1478,1689,2614,1383,2480,1832,3101,2833,2290,1642,1452,2643, 2453,1805,1262,994,2263,1615,2712,1481,2406,2617,1400,967,3588,2237,886,1701,3331,3264, 2828,1373,1458,3169,941,2638,2504,1811,1744,751,2409,3210,1649,1431,3156,984,3115,2724, 1269,889,1690,2396,1860,2467,1595,509,3102,2834,2753,1215,947,2672,2454,1806,2359,2292, 1644,2699,1482,2645,2618,1387,996,3217,2238,1702,3360,2591,1374,2457,1921,3170,942,226 7,1840,1731,3333,2410,1650,1460,3143,971,3592,1813,1270,890,1705,2383,3212,1623,2944,14 89,510,3 117,2849,2754,863,1692,2659,2469,1597,1435,3160,2836,2279,2728,1273,949,2646,25 12,1864,759,2417,3218,2701,1484,3123,2620,1389,2458,1922,2363,2296,1827,1760,3334,2649, 1447,3172,1000,2269,1814,1733,1706,2412,1652,2707,1490,973,3118,2850,1395,892,1679,333 7,2470,1598,1464,3147,2823,2756,1817,1274,950,2661,2499,1627,1437,2418,3233,2702,1247,9 79,3600,2607,1390,2473,1713,2391,3220,2840,2283,3125,953,2650,2460,1924,763,2365,2270,1 829,1734,3392,2175,1639,2736,1505,974,1872,879,1708,3338,2709,1492,1451,3176,2852,1397, 1818,1737,2662,2528,1656,1438,3149,2881,3234,1343,1276,1008,3587,2501,1629,2474,1714,2 420,3207,2827,2760,981,3126,954,2665,2447,1687,3345,2366,2285,1830,3155,927,2652,2723,1 506,765,2395,3224,1859,3129,2710,1479,1928,2615,1398,2481,1833,1738,3340,2291,1643,145 3,3150,2882,1820,1263,995,3616,2502,1630,2713,1496,2407,3236,2856,1401,982,3589,2666,24 76,887,1716,3346,3265,2829,2286,1459,3184,956,2639,2505,1745,766,2424,3211,1888,3157,98 5,3130,2725,1508,1691,2397,1861,2482,1834,3103,2835,2768,1454,2673,2455,1807,1740,2293, 1645,2714,1483,2884,2619,1402,997,3590,3456,2239,1703,3361,3266,2830,1375,1936,3171,94 3,2668,2506,1841,1746,3348,2411,3240,1651,1461,3158,986,3593,2726,1271,891,1720,2398,32 13,1862,2945,511,3132,2864,2755,1693,2674,2484,1836,3161,2837,2294,1646,2729,1512,2647, 2513,1865,998,3219,2716,1485,3362,2621,1404,2459,1923,3648,2297,1842,1761,3335,3268,28 88,1462,3173,1001,3594,2508,1815,1748,1707,2413,3214,1653,2946,1491,988,3119,2851,2784, 893,1694,3352,2471,1599,1465,3162,2838,2757,2730,1275,951,2676,2514,1866,2419,3248,270 3,1486,3601,2622,1391,2488,1952,3221,2841,2298,1762,3364,2651,2461,1925,3174,1002,2271, 1844,1735,3393,2414,1654,2737,1520,975,3596,1873,894,1709,3339,3272,2948,1493,1466,317 7,2853,2758,1819,1752,2663,2529,1657,1439,3164,2896,3235,2732,1277,1009,3602,2516,1868, 2475,1715,2421,3222,2842,2761,3127,955,2680,2462,1926,2367,2300,1831,1764,3394,2653,27 38,1507,1004,3225,1874,1710,3368,2711,1494,1929,3178,2854,1399,1848,1739,3341,2530,165 8,1468,3151,2883,3712,1821,1278,1010,3617,2503,1631,2952,1497,2422,3237,2857,2762,983,3 604,2667,2477,1717,3347,3280,2844,2287,3185,957,2654,2520,1984,767,2425,3226,1889,3396, 3131,2740,1509,1930,1876,2483,1835,1768,3342,2769,1455,3180,2912,1822,1741,3618,2532,1 660,2715,1498,2885,3238,2858,1403,1012,3591,3457,2478,1718,3376,3267,2831,2764,1937,31 86,958,2669,2507,1747,3349,2426,3241,1890,3159,987,3608,2727,1510,1721,2399,3228,1863,2 960,3133,2865,2770,1932,2675,2485,1837,1742,3400,2295,1647,2744,1513,2886,1880,999,362 0,3458,2717,1500,3363,3296,2860,1405,1938,3649,2670,2536,1843,1776,3350,3269,2889,3242, 1463,3188,1016,3595,2509,1749,1722,2428,3215,1892,2947,989,3134,2866,2785,1695,3353,24 86,1838,3163,2839,2772,2731,1514,2677,2515,1867,3249,2718,1487,3840,2623,1406,2489,195 3,3650,3460,2299,1763,3365,3270,2890,1940,3175,1003,3624,2510,1845,1750,3408,2415,3244, 1655,2976,1521,990,3597,2786,895,1724,3354,3273,2949,1467,3192,2868,2759,1753,2678,254 4,1896,3165,2897,3250,2733,1516,3603,2517,1869,2490,1954,3223,2843,2776,3366,2681,2463, 1927,3652,2301,1846,1765,3395,2892,2739,1522,1005,3598,3464,1875,1711,3369,3274,2950,1 495,1944,3179,2855,2788,1849,1754,3356,2531,1659,1469,3166,2898,3713,2734,1279,1011,36 32,2518,1870,2953,2423,3252,2872,2763,3605,2682,2492,1956,3281,2845,2302,1766,3424,265 5,2521,1985,1006,3227,1904,3397,3370,2741,1524,1931,3656,1877,1850,1769,3343,3276,3008, 1470,3181,2913,3714,1823,1756,3619,2533,1661,2954,1499,2900,3239,2859,2792,1013,3606,3 472,2479,1719,3377,3282,2846,2765,3187,959,2684,2522,1986,2427,3256,1891,3398,3609,274 2,1511,1960,3229,1878,2961,1770,3372,2771,1933,3182,2914,1852,1743,3401,2534,1662,2745, 1528,2887,3716,1881,1014,3621,3459,2956,1501,3378,3297,2861,2766,1939,3664,2671,2537,1 777,3351,3284,2904,3243,3189,1017,3610,2524,1988,1723,2429,3230,1893,2962,3135,2867,28 00,1934,2487,1839,1772,3402,2773,2746,1515,2916,1882,3622,3488,2719,1502,3841,3298,286 2,1407,1968,3651,3461,2538,1778,3380,3271,2891,3720,1941,3190,1018,3625,2511,1751,3409, 2430,3245,1894,2977,991,3612,2787,1725,3355,3288,2964,3193,2869,2774,1992,2679,2545,18 97,3404,3251,2748,1517,3842,1884,2491,1955,3680,3462,2777,3367,3300,2920,1942,3653,362 6,2540,1847,1780,3410,2893,3246,2978,1523,1020,3599,3465,1726,3384,3275,2951,1945,3194, 2870,2789,1755,3357,2546,1898,3167,2899,3728,2735,1518,3633,2519,1871,2968,3253,2873,2 778,3844,2683,2493,1957,3654,3520,2303,1767,3425,2894,2000,1007,3628,3466,1905,3412,33 71,3304,2980,1525,1946,3657,2790,1851,1784,3358,3277,3009,1471,3196,2928,3715,1757,363 4,2548,1900,2955,2901,3254,2874,2793,3607,3473,2494,1958,3283,2847,2780,3426,2685,2523, 1987,3257,1906,3399,3848,2743,1526,1961,3658,3468,1879,1771,3373,3278,3010,1948,3183,2 915,3744,1853,1758,3416,2535,1663,2984,1529,2902,3717,2794,1015,3636,3474,2957,3379,33 12,2876,2767,3665,2686,2552,2016,3285,2905,3258,3428,3611,2525,1989,1962,3231,1908,296 3,3374,2801,1935,3660,1854,1773,3403,3012,2747,1530,2917,3718,1883,3623,3489,2958,1503, 3856,3299,2863,2796,1969,3666,3476,2539,1779,3381,3286,2906,3721,3191,1019,3640,2526,1 990,2431,3260,1895,2992,3613,2802,1964,3289,2965,1774,3432,2775,1993,2918,1912,3405,34 90,2749,1532,3843,3776,1885,1970,3681,3463,3016,3382,3301,2921,3722,1943,3668,3627,254 1,1781,3411,2908,3247,2979,1021,3614,3480,1727,3385,3290,2966,3195,2871,2804,1994,2547, 1899,3406,3729,2750,1519,3872,1886,2969,3682,3492,2779,3845,3302,2922,1972,3655,3521,2 542,1782,3440,2895,3724,2001,1022,3629,3467,3413,3386,3305,2981,1947,3672,2791,1785,33 59,3292,3024,3197,2929,3730,1996,3635,2549,1901,2970,3255,2875,2808,3846,2495,1959,368 4,3522,2781,3427,2924,2002,3630,3496,1907,3414,3849,3306,2982,1527,1976,3659,3469,1786, 3388,3279,3011,1949,3198,2930,3745,1759,3417,2550,1902,2985,2903,3732,2795,3637,3475,2 972,3313,2877,2782,3904,2687,2553,2017,3524,3259,3429,3850,2004,1963,3688,3470,1909,33 75,3308,3040,1950,3661,3746,1855,1788,3418,3013,2986,1531,2932,3719,3638,3504,2959,385 7,3314,2878,2797,3667,3477,2554,2018,3287,2907,3736,3430,3641,2527,1991,3261,1910,2993, 3852,2803,1965,3662,3528,1775,3433,3014,2008,2919,3748,1913,3420,3491,2988,1533,3858,3 777,2798,1971,3696,3478,3017,3383,3316,2936,3723,3669,3642,2556,2020,2909,3262,2994,36 15,3481,1966,3291,2967,3434,2805,1995,1914,3407,3968,2751,1534,3873,3778,1887,3683,349 3,3018,3860,3303,2923,3752,1973,3670,3536,2543,1783,3441,2910,3725,1023,3644,3482,3387, 3320,2996,3673,2806,2024,3293,3025,3436,3731,1997,3874,1916,2971,3494,2809,3847,3780,1 974,3685,3523,3020,3442,2925,3726,2003,3631,3497,3415,3864,3307,2983,1977,3674,3484,17 87,3389,3294,3026,3199,2931,3760,1998,2551,1903,3000,3733,2810,3876,2973,3686,3552,278 3,3905,2926,2032,3525,3498,3444,3851,3784,2005,1978,3689,3471,3390,3309,3041,1951,3676, 3747,1789,3419,3028,2987,2933,3734,3639,3505,2974,3315,2879,2812,3906,2555,2019,3526,3 737,3431,3880,2006,3690,3500,1911,3853,3310,3042,1980,3663,3529,1790,3448,3015,2009,29 34,3749,3421,3506,2989,3859,3792,2799,3697,3479,3032,3317,2937,3738,3908,3643,2557,202 1,3263,2995,3854,1967,3692,3530,3435,3044,2010,3750,1915,3422,3969,2990,1535,3888,3779, 3698,3508,3019,3861,3318,2938,3753,3671,3537,2558,2022,2911,3740,3645,3483,3321,2997,3 912,2807,2025,3532,3437,3970,2012,3875,3808,1917,3495,3048,3862,3781,3754,1975,3700,35 38,3021,3443,2940,3727,3646,3512,3865,3322,2998,3675,3485,2026,3295,3027,3438,3761,199 9,1918,3001,3972,2811,3877,3782,3687,3553,3022,3920,2927,3756,2033,3540,3499,3445,3866, 3785,1979,3704,3486,3391,3324,3056,3677,3762,2028,3029,3002,3735,3878,2975,3554,2813,3 907,2034,3527,3976,3446,3881,3786,2007,3691,3501,3868,3311,3043,1981,3678,3544,1791,34 49,3030,2935,3764,3507,3004,3793,2814,3936,3033,3556,3739,3909,3882,2036,3502,3855,378 8,1982,3693,3531,3450,3045,2011,3751,3423,3984,2991,3889,3794,3699,3509,3034,3319,2939, 3768,3910,2559,2023,3741,3884,3694,3560,3913,3046,2040,3533,3452,3971,2013,3890,3809,3 510,3049,3863,3796,3755,3701,3539,3036,2941,3742,3647,3513,3323,2999,3914,2027,3534,34 39,4000,2014,3810,1919,3973,3050,3892,3783,3702,3568,3023,3921,2942,3757,3541,3514,386 7,3800,3705,3487,3325,3057,3916,3763,2029,3003,3974,3879,3812,3555,3052,3922,3758,2035, 3542,3977,3447,3896,3787,3706,3516,3869,3326,3058,3679,3545,2030,3031,3765,3005,4032,2 815,3937,3557,3978,3924,3883,3816,2037,3503,3870,3789,1983,3708,3546,3451,3060,3766,39 85,3006,3795,3938,3035,3558,3769,3911,2038,3980,3885,3790,3695,3561,3928,3047,2041,354 8,3453,3986,3891,3824,3511,3064,3797,3770,3940,3037,3743,3886,3562,3915,2042,3535,3454, 4001,2015,3811,3988,3051,3893,3798,3703,3569,3038,2943,3772,3515,3801,3944,3564,3917,4 002,2044,3975,3894,3813,3570,3053,3923,3759,3543,3992,3897,3802,3707,3517,3327,3059,39 18,2031,4004,3814,4033,3054,3952,3572,3979,3925,3898,3817,3518,3871,3804,3709,3547,306 1,3767,3007,4034,3939,3559,4008,3926,3818,2039,3981,3900,3791,3710,3576,3929,3062,3549, 3987,3825,3065,4036,3771,3941,3982,3887,3820,3563,3930,2043,3550,3455,4016,3826,3989,3 066,3799,3942,3039,3773,4040,3945,3565,3932,4003,2045,3990,3895,3828,3571,3068,3774,39 93,3803,3946,3566,3919,2046,4005,3815,4048,3055,3953,3573,3994,3899,3832,3519,3805,394 8,4006,4035,3954,3574,4009,3927,3819,3996,3901,3806,3711,3577,3063,4064,4037,4010,3956, 3983,3902,3821,3578,3931,3551,4017,3827,3067,4038,3943,4012,3822,4041,3960,3580,3933,4 018,3991,3829,3069,3775,4042,3947,3567,3934,2047,4020,3830,4049,3070,3995,3833,4044,39 49,4007,4050,3955,3575,4024,3834,3997,3807,3950,4065,4052,4011,3957,3998,3903,3836,357 9,4066,4039,3958,4013,3823,4056,3961,3581,4019,4068,4014,4043,3962,3582,3935,4021,3831, 3071,4072,4045,3964,4022,4051,4025,3835,4046,3951,4080,4053,4026,3999,3837,4067,4054,3 959,4028,3838,4057,4069,4015,4058,3963,3583,4070,4073,4060,3965,4023,4074,4047,3966,40 81,4027,4076,4082,4055,4029,3839,4084,4030,4059,4071,4088,4061,4075,4062,3967,4077,408 3,4078,4085,4031,4086,4089,4090,4063,4092,4079,4087,4091,4093,4094,4095,],
• wherein sequence Q2=[6309,5445,6419,5391,6298,6203,5667,5287,6414,5654,6252,5425,5330,5235,6310,6663,5446, 5657,6339,5277,3623,6258,5420,4819,6421,5230,6313,6231,5449,3381,3721,6300,4935,6205,5 669,5507,5004,5426,5345,4909,4814,3613,3289,5399,5332,5291,6692,5237,5658,6435,5278,34 05,5010,5183,4915,6422,6341,6314,3681,6260,3463,6667,5450,4821,3382,3301,4794,3722,628 7,4964,3668,3627,6206,5670,3411,4767,6425,3247,2979,5346,4910,3614,6235,3480,5699,5509, 4586,3385,3290,5428,2966,5319,4939,5768,3195,5238,6321,5673,4559,7180,5457,4478,5293,3 406,5025,6722,3729,6532,5660,4835,6437,6342,5403,2969,5336,5012,3682,6247,3492,6696,52 41,2779,4917,4822,3845,6480,3302,2922,6316,4727,4593,3655,7186,3521,6669,5452,5299,344 0,4796,2895,6426,3724,6345,4539,3629,6264,3467,5728,5510,3413,4825,3386,3305,5415,2981, 5348,4968,1947,3672,6237,5701,2791,6322,5674,4588,3359,3292,6675,5458,4941,5294,3197,5 026,2929,3730,6295,5647,5513,3635,6438,2549,1901,5432,2970,5323,4999,6724,3255,2875,52 42,4918,4837,3846,6467,5405,2495,1959,4594,3684,7201,3522,6670,5215,2781,6536,4947,577 6,3427,4783,2924,6441,6346,5681,2002,4567,7188,5016,3630,6251,3496,1907,5301,3414,4921, 4826,3849,6428,3306,5892,2982,1527,4731,1976,4541,3659,6238,3469,5702,6785,5568,1786,4 351,3388,3279,6704,5473,3011,4942,1949,3198,2930,3745,6324,5676,1759,5514,3417,6677,54 60,2550,1902,5419,2985,5352,5028,2903,3732,6353,5705,2795,4838,3637,6496,3475,5406,297 2,5325,5057,7202,3313,2877,5244,2782,6299,4976,5763,6469,2687,6442,2553,5682,2017,4596, 7175,3524,5003,6728,3259,4949,5302,3429,4922,4841,3850,6415,6348,5655,2004,5521,1963,4 542,3688,6253,3470,1909,6786,5331,4895,4828,3375,3308,6691,5474,3040,4733,1950,4571,36 61,7192,3746,6311,1855,1788,5305,3418,6678,5447,3013,6544,5896,2986,1531,4791,2932,644 9,3719,6354,5706,5516,3638,6259,3504,5421,2959,5326,5058,3857,3314,2878,5231,2797,6328, 4963,5792,3667,6470,3477,6681,5464,2554,2018,4583,7204,3287,5032,2907,3736,6301,4950,5 765,3430,4842,3641,6444,2527,5684,1991,5522,7233,5005,6254,3261,1910,5427,2993,5360,49 24,4815,3852,6473,5713,2803,4734,1965,4600,3662,7179,3528,6788,5333,4953,1775,5306,343 3,6693,5476,3014,6531,5659,2008,4573,2919,6450,3748,6369,1913,5279,3420,5011,6736,3491, 5422,2988,1533,4849,3858,6423,3777,6356,5708,2798,6315,1971,3696,6261,3478,6682,5451,3 017,5060,3383,3316,4795,2936,3723,6302,4965,5766,3669,3642,6207,2556,5671,2020,5537,72 34,5006,2909,3262,5904,2994,5347,4911,4844,3615,6474,3481,5714,5524,1966,4587,7208,329 1,5429,2967,5334,4954,5769,3434,6694,5239,2805,6560,5688,1995,4574,7181,6913,6370,1914, 4479,5308,3407,5040,6723,3968,6533,5661,2751,1534,4850,3873,6452,3778,6343,1887,6792,5 337,5013,3683,6262,3493,6697,5480,3018,4823,3860,6481,3303,2923,3752,6317,4966,1973,36 70,7187,3536,6684,5453,2543,1783,5538,3441,4797,2910,6427,3725,6360,5891,5824,1023,364 4,6265,3482,5729,5511,7236,5064,3387,3320,5430,2996,5349,4969,5770,3673,6476,5716,2806, 6323,5675,2024,4589,7182,3293,6914,5459,3025,4956,5295,3436,5027,6752,3731,6534,5662,1 997,5528,3874,6439,6372,1916,5433,2971,5338,5014,6725,3494,6698,5243,2809,4919,4852,38 47,6482,3780,7297,6318,1974,4595,3685,7216,3523,6671,5454,3020,6537,5777,3442,4798,292 5,6456,3726,6347,5920,2003,7189,5017,3631,6266,3497,5730,5540,3415,4827,3864,6429,3307, 5893,2983,5350,4970,1977,3674,6239,3484,5703,6800,5569,1787,4590,3389,3294,6705,5488,3 026,4943,5772,3199,2931,3760,6325,5677,1998,5515,7240,6916,5461,2551,1903,5434,3000,53 53,5029,6726,3733,6592,5720,2810,4839,3876,6497,7298,5407,2973,5340,5072,3686,7203,355 2,6700,5245,2783,6538,4977,5778,3905,6484,2926,6443,6376,5683,2032,4597,7190,3525,5018, 6729,3498,5303,3444,4923,4856,3851,6430,3784,6349,5894,2005,1978,4543,3689,6268,3471,5 732,6787,5570,4829,3390,3309,6706,5475,3041,4972,1951,3676,7193,3747,6326,5678,1789,55 44,3419,6679,5462,3028,6545,5897,2987,5354,5030,2933,3734,6355,5707,5517,3639,6498,350 5,5436,2974,5327,5059,3315,2879,5246,2812,6329,4978,5793,3906,6471,7300,6920,5465,2555, 2019,4598,7205,3526,5033,6730,3737,6540,4951,5780,3431,4843,3880,6350,5685,2006,5523,7 248,5020,3690,6255,3500,1911,6816,5361,4925,4830,3853,6488,3310,5952,3042,4735,1980,46 01,3663,7194,3529,6789,5572,1790,5307,3448,6708,5477,3015,6546,5898,2009,2934,3749,638 4,5736,5518,3421,3506,5423,2989,5356,5088,3859,3792,2799,5794,3697,6500,3479,5466,3032, 5061,3317,5034,2937,3738,4980,3908,7425,3643,2557,2021,5552,5007,3263,5905,2995,5362,4 926,4845,3854,7304,1967,4602,3692,3530,5335,4955,5784,3435,3044,2010,4575,6928,3750,19 15,5309,3422,5041,3969,5900,2990,1535,4851,3888,3779,5576,3698,3508,3019,5062,3318,293 8,4967,7426,3537,2558,2022,7264,5036,2911,3740,4846,3645,3483,5744,3321,2997,4984,3912, 2807,2025,4604,3532,6848,3437,3970,2012,3808,1917,3048,7312,1975,3021,6016,2940,7428,3 512,2998,2026,6944,1918,3972,3920,3056,7681,6445,6451,6737,6357,5709,6330,6683,7206,63 03,5767,6446,5686,7235,6732,6475,5715,5525,7209,6790,6695,5478,6561,5689,7196,6371,673 8,6548,6453,6358,5710,6793,6263,6712,5481,3861,3753,6332,5796,3671,6685,5468,5539,6361, 5906,5825,6504,5526,7237,5065,7210,5431,5364,5771,6477,5717,6562,5690,7183,6915,4957,5 310,5042,6753,6535,5663,5529,3875,6454,6373,6794,5339,5015,6740,3495,6699,5482,4853,38 62,6483,3781,3754,6319,3700,7217,3538,6686,5455,6552,3443,4799,6457,3727,6362,5921,582 6,3646,6267,5731,5541,7238,5066,3865,3322,5908,5351,4971,5800,3675,6478,3485,5718,6801, 5584,4591,7212,3295,5489,3027,4958,5773,3438,6754,3761,6564,5692,1999,5530,7241,6917,6 374,5435,3001,5368,5044,6727,6593,5721,2811,4854,3877,6512,3782,7299,6796,5341,5073,36 87,7218,3553,6701,5484,3022,6539,5779,6485,2927,6458,3756,6377,5922,2033,7191,3540,501 9,6744,3499,5542,3445,4857,3866,6431,3785,6364,5895,5828,1979,3704,6269,3486,5733,6802, 5571,5068,3391,3324,6707,5490,4973,5774,3677,7432,3762,6327,5679,2028,5545,7242,6918,5 463,3029,5912,3002,5355,5031,6756,3735,6594,5722,5532,3878,6499,7328,5437,2975,5342,50 74,3554,6702,5247,2813,6568,4979,5808,3907,6486,7301,6921,6378,2034,4599,7220,3527,504 8,6731,3976,6541,5781,3446,4858,3881,6460,3786,6351,5924,2007,7249,5021,3691,6270,3501, 5734,6817,5600,4831,3868,6489,3311,5953,3043,4974,1981,3678,7195,3544,6804,5573,1791,5 546,3449,6709,5492,3030,6547,5899,5832,2935,3764,6385,5737,5519,7244,6976,3507,5438,30 04,5357,5089,7682,3793,6596,5724,2814,6331,5795,3936,6501,7302,6922,5467,3033,5076,720 7,3556,5035,6760,3739,6542,4981,5782,3909,7440,3882,6447,6380,5687,2036,5553,7250,5022, 6733,3502,6818,5363,4927,4860,3855,6490,3788,7305,5954,1982,4603,3693,7224,3531,6791,5 574,5785,3450,6710,5479,3045,6576,5928,2011,7197,6929,3751,6386,5738,5548,3423,6739,39 84,6549,5901,2991,5358,5090,3889,3794,6359,5711,6808,5577,3699,6502,3509,6713,5496,303 4,5063,7684,3319,2939,3768,6333,4982,5797,3910,7427,7360,6924,5469,2559,2023,5554,7265, 5037,6734,3741,6600,5907,5840,4847,3884,6505,7306,5745,5527,7252,5080,3694,7211,3560,6 820,5365,4985,5786,3913,6492,5956,3046,6563,5691,2040,4605,7198,3533,6930,6849,5311,34 52,5043,6768,3971,6550,5902,2013,3890,6455,3809,6388,5740,6795,5578,6741,3510,6714,548 3,3049,5092,3863,3796,7313,3755,6334,5798,3701,7456,3539,6687,5470,3036,6553,6017,7266, 5038,2941,3742,6363,5936,5827,7429,3647,6506,3513,5746,5556,7239,5067,7688,3323,5909,2 999,5366,4986,5801,3914,6479,7308,5719,7040,5585,2027,4606,7213,3534,6945,6850,4959,57 88,3439,6755,4000,6565,5693,2014,5531,7256,6932,3810,6375,1919,6824,5369,5045,6742,397 3,6608,5960,3050,4855,3892,6513,3783,7314,6797,5580,3702,7219,3568,6716,5485,3023,6554, 6018,3921,2942,6459,3757,6392,5923,5856,7430,3541,6745,3514,5543,7268,5096,3867,3800,6 365,5910,5829,5802,3705,6508,3487,5748,6803,5586,5069,7214,3325,6946,5491,3057,4988,57 75,3916,7433,3763,6566,5694,2029,5560,7243,6919,6852,5913,3003,5370,5046,6757,3974,659 5,5723,5533,3879,6514,3812,7329,6798,5343,5075,7696,3555,6703,5486,3052,6569,5809,3922, 6487,7316,6936,3758,6379,2035,7221,3542,5049,6746,3977,6556,6020,3447,4859,3896,6461,3 787,6366,5925,5830,7488,3706,6271,3516,5735,6832,5601,5070,3869,3326,5968,3058,4975,58 04,3679,7434,3545,6805,5588,2030,5547,7272,6948,5493,3031,5914,5833,6758,3765,6624,575 2,5534,7245,6977,7330,5439,3005,5372,5104,7683,4032,6597,5725,2815,6570,5810,3937,6516, 7303,6923,6856,5077,7222,3557,5050,6761,3978,6543,5783,3924,7441,3883,6462,3816,6381,5 926,2037,7251,5023,6748,3503,6819,5602,4861,3870,6491,3789,7320,5955,1983,3708,7225,35 46,6806,5575,6024,3451,6711,5494,3060,6577,5929,5834,7436,3766,6387,5739,5549,7246,697 8,3985,5916,3006,5359,5091,7712,3795,6598,5726,6809,5592,3938,6503,7332,6952,5497,3035, 5078,7685,3558,6762,3769,6572,4983,5812,3911,7442,7361,6925,6382,2038,5555,7280,5052,6 735,3980,6601,5841,4862,3885,6520,3790,7307,5984,7253,5081,3695,7226,3561,6821,5604,57 87,3928,6493,5957,3047,6578,5930,2041,7199,3548,6931,6864,5550,3453,6769,3986,6551,590 3,5836,3891,3824,6389,5741,6810,5579,6980,3511,6715,5498,3064,5093,7686,3797,7552,3770, 6335,5799,3940,7457,7362,6926,5471,3037,6032,7267,5039,6764,3743,6602,5937,5842,7444,3 886,6507,7336,5747,5557,7254,5082,7689,3562,6822,5367,4987,5816,3915,6494,7309,5958,70 41,2042,4607,7228,3535,6960,6851,5789,3454,6770,4001,6580,5932,2015,7257,6933,3811,639 0,5742,6825,5608,6743,3988,6609,5961,3051,5094,3893,3798,7315,6812,5581,3703,7458,3569, 6717,5500,3038,6555,6019,7744,2943,3772,6393,5938,5857,7431,7364,6984,3515,5558,7269,5 097,7690,3801,6604,5911,5844,5803,3944,6509,7310,5749,7042,5587,5084,7215,3564,6947,68 80,4989,5790,3917,7448,4002,6567,5695,2044,5561,7258,6934,6853,6826,5371,5047,6772,397 5,6610,5962,3894,6515,3813,7344,6799,5582,7697,3570,6718,5487,3053,6584,6048,3923,7317, 6937,3759,6394,5858,7460,3543,6747,3992,6557,6021,7270,5098,3897,3802,6367,5940,5831,7 489,3707,6510,3517,5750,6833,5616,5071,7692,3327,5969,3059,4990,5805,3918,7435,7368,70 44,5589,2031,5562,7273,6949,6854,5915,5848,6759,4004,6625,5753,5535,7260,6992,3814,733 1,6828,5373,5105,7698,4033,6612,5964,3054,6571,5811,3952,6517,7318,6938,6857,7223,3572, 5051,6776,3979,6558,6022,3925,3898,6463,3817,6396,5927,5860,7490,6749,3518,6834,5603,5 100,3871,3804,7321,5970,5806,3709,7464,3547,6807,5590,6025,7274,6950,5495,3061,5944,58 35,7437,3767,6626,5754,5564,7247,6979,7808,5917,3007,5374,5106,7713,4034,6599,5727,704 8,5593,3939,6518,7333,6953,6858,5079,7700,3559,6763,4008,6573,5813,3926,7443,7376,6940, 3818,6383,2039,7281,5053,6750,3981,6616,6080,4863,3900,6521,3791,7322,5985,7492,3710,7 227,3576,6836,5605,6026,3929,5972,3062,6579,5931,5864,7438,3549,6865,5551,7276,7008,39 87,5918,5837,7714,3825,6628,5756,6811,5594,6981,7334,6954,5499,3065,5108,7687,4036,755 3,3771,6574,5814,3941,7472,7363,6927,6860,6033,7282,5054,6765,3982,6603,5843,7445,3887, 6522,3820,7337,5986,7255,5083,7704,3563,6823,5606,5817,3930,6495,7324,5959,7056,2043,7 229,3550,6961,6866,6028,3455,6771,4016,6581,5933,5838,7496,3826,6391,5743,6840,5609,69 82,3989,5976,3066,5095,7716,3799,7554,6813,5596,3942,7459,7392,6956,5501,3039,6034,774 5,6766,3773,6632,5939,5872,7446,7365,6985,7338,5559,7284,5112,7691,4040,6605,5845,5818, 3945,6524,7311,5988,7043,5085,7230,3565,6962,6881,5791,3932,7449,4003,6582,5934,2045,7 259,6935,6868,6827,5610,6773,3990,6611,5963,3895,3828,7345,6814,5583,7936,3571,6719,55 02,3068,6585,6049,7746,7556,3774,6395,5859,7461,7366,6986,3993,6036,7271,5099,7720,380 3,6606,5941,5846,7504,3946,6511,7340,5751,7072,5617,5086,7693,3566,6882,4991,5820,3919, 7450,7369,7045,2046,5563,7288,6964,6855,5849,6774,4005,6640,5992,7261,6993,3815,7346,6 829,5612,7699,4048,6613,5965,3055,6586,6050,3953,7319,6939,6872,7462,3573,6777,3994,65 59,6023,7748,3899,3832,6397,5942,5861,7491,6988,3519,6835,5618,5101,7694,3805,7560,597 1,5807,3948,7465,7370,7046,5591,6040,7275,6951,6884,5945,5850,7452,4006,6627,5755,5565, 7262,6994,7809,6830,5375,5107,7728,4035,6614,5966,7049,3954,6519,7348,6968,6859,7701,3 574,6778,4009,6588,6052,3927,7377,6941,3819,6398,5862,7520,6751,3996,6617,6081,5102,39 01,3806,7323,6000,7493,3711,7466,3577,6837,5620,6027,7752,5973,3063,5946,5865,7439,737 2,7104,5566,7277,7009,7810,5919,5852,7715,4064,6629,5757,7050,5595,6996,7335,6955,6888, 5109,7702,4037,7568,4010,6575,5815,3956,7473,7378,6942,6861,7283,5055,6780,3983,6618,6 082,3902,6523,3821,7352,5987,7494,7705,3578,6838,5607,6056,3931,7325,5974,7057,5866,74 68,3551,6867,6029,7278,7010,4017,5948,5839,7497,3827,6630,5758,6841,5624,6983,7812,597 7,3067,5110,7717,4038,7555,7052,5597,3943,7474,7393,6957,6862,6035,7760,6767,4012,6633, 5873,7447,7380,7000,3822,7339,7285,5113,7706,4041,6620,6084,5819,3960,6525,7326,5989,7 058,7231,3580,6963,6896,6030,3933,4018,6583,5935,5868,7498,6869,6842,5611,7012,3991,59 78,7718,3829,7584,6815,5598,7937,7394,6958,5503,3069,6064,7747,7557,3775,6634,5874,747 6,7367,6987,7816,6037,7286,5114,7721,4042,6607,5847,7505,3947,6526,7341,5990,7073,5087, 7708,3567,6883,5821,3934,7451,7384,7060,2047,7289,6965,6870,6088,6775,4020,6641,5993,7 500,3830,7347,6844,5613,7938,4049,5980,3070,6587,6051,7776,7558,6873,7463,7396,7016,39 95,6038,7749,7722,3833,6636,5943,5876,7506,6989,7342,7074,5619,5116,7695,4044,7561,582 2,3949,7480,7371,7047,6041,7290,6966,6885,5851,7453,4007,6642,5994,7263,6995,7824,6831, 5614,7729,4050,6615,5967,7064,3955,7349,6969,6874,7940,3575,6779,4024,6589,6053,7750,7 616,3834,6399,5863,7521,6990,3997,6096,5103,7724,3807,7562,6001,7508,3950,7467,7400,70 76,5621,6042,7753,6886,5947,5880,7454,7373,7105,5567,7292,7024,7811,5853,7730,4065,664 4,5996,7051,6997,7350,6970,6889,7703,4052,7569,4011,6590,6054,3957,7379,6943,6876,7522, 6781,3998,6619,6083,3903,3836,7353,6002,7495,7944,3579,6839,5622,6057,7754,7564,5975,5 867,7469,7374,7106,6044,7279,7011,7840,5949,5854,7512,4066,6631,5759,7080,5625,6998,78 13,6890,5111,7732,4039,7570,7053,3958,7475,7408,6972,6863,7761,6782,4013,6648,6112,738 1,7001,3823,7354,7524,7707,4056,6621,6085,6058,3961,7327,6004,7059,7470,3581,6897,6031, 7756,4019,5950,5869,7499,7108,6843,5626,7013,7814,5979,7719,4068,7585,7054,5599,7952,7 395,6959,6892,6065,7762,7572,4014,6635,5875,7477,7382,7002,7817,7287,5115,7736,4043,66 22,6086,3962,6527,7356,5991,7088,7709,3582,6898,6060,3935,7385,7061,5870,7528,6871,608 9,7014,4021,6008,7501,3831,7586,6845,5628,7939,7872,5981,3071,6066,7777,7559,7112,7478, 7397,7017,7818,6039,7764,7723,4072,6637,5877,7507,7004,7343,7075,5117,7710,4045,7576,5 823,3964,7481,7386,7062,7291,6967,6900,6090,4022,6643,5995,7502,7825,6846,5615,7968,40 51,5982,7065,7778,7588,6875,7941,7398,7018,4025,6068,7751,7617,3835,6638,5878,7536,699 1,7820,6097,5118,7725,4046,7563,7509,3951,7482,7401,7077,6043,7768,6887,5881,7455,7388, 7120,7293,7025,7826,6092,7731,4080,6645,5997,7066,7351,6971,6904,7942,4053,4026,6591,6 055,7780,7618,6877,7523,7020,3999,6098,7726,3837,7592,6003,7510,7945,7402,7078,5623,60 72,7755,7565,5882,7484,7375,7107,6045,7294,7026,7841,5855,7513,4067,6646,5998,7081,699 9,7828,6891,7733,4054,7571,7068,3959,7409,6973,6878,8000,6783,4028,6649,6113,7620,3838, 7355,7525,7946,4057,6100,6059,7784,7566,6005,7471,7404,7136,6046,7757,7842,5951,5884,7 514,7109,7082,5627,7028,7815,7734,4069,7600,7055,7953,7410,6974,6893,7763,7573,4015,66 50,6114,7383,7003,7832,7526,7737,4058,6623,6087,3963,7357,6006,7089,7948,3583,6899,606 1,7758,7624,5871,7529,7110,6104,7015,7844,6009,7516,4070,7587,7084,5629,7954,7873,6894, 6067,7792,7574,7113,7479,7412,7032,7819,7765,7738,4073,6652,6116,7005,7358,7090,7711,4 060,7577,6062,3965,7387,7063,7530,6901,6091,4023,6010,7503,8064,6847,5630,7969,7874,59 83,7779,7589,7114,7956,7399,7019,7848,6069,7766,7632,4074,6639,5879,7537,7006,7821,511 9,7740,4047,7578,3966,7483,7416,7092,7769,6902,6120,7389,7121,7532,7827,6093,7970,4081, 6012,7067,7590,6905,7943,7876,4027,6070,7781,7619,7116,7538,7021,7822,6099,7727,4076,7 593,7511,7960,7403,7079,6073,7770,7580,5883,7485,7390,7122,7295,7027,7856,6094,4082,66 47,5999,7096,7829,6906,7972,4055,7069,7782,7648,6879,8001,7022,4029,6128,7621,3839,759 4,7540,7947,7880,6101,6074,7785,7567,7486,7405,7137,6047,7772,7843,5885,7515,7124,7083, 7029,7830,7735,4084,7601,7070,7411,6975,6908,8002,4030,6651,6115,7622,7833,7527,7976,4 059,6102,7786,7596,6007,7949,7406,7138,6076,7759,7625,5886,7544,7111,6105,7030,7845,75 17,4071,7602,7085,7955,7888,6895,7793,7575,7128,7413,7033,7834,8004,7739,4088,6653,611 7,7359,7091,7950,4061,6063,7788,7626,7531,7140,6106,7846,6011,7518,8065,7086,5631,7984, 7875,7794,7604,7115,7957,7414,7034,7849,7767,7633,4075,6654,6118,7007,7836,7741,4062,7 579,3967,7417,7093,8008,6903,6121,7628,7533,8066,6108,7971,7904,6013,7591,7144,7958,78 77,7850,6071,7796,7634,7117,7539,7036,7823,7742,4077,7608,7961,7418,7094,7771,7581,612 2,7391,7123,7534,7857,6095,4083,6014,7097,8068,6907,7973,7878,7783,7649,7118,8016,7023, 7852,6129,7636,4078,7595,7541,7962,7881,6075,7800,7582,7487,7420,7152,7773,7858,6124,7 125,7098,7831,7974,4085,7071,7650,6909,8003,4031,6130,7623,8072,7542,7977,7882,6103,77 87,7597,7964,7407,7139,6077,7774,7640,5887,7545,7126,7031,7860,4086,7603,7100,7889,691 0,8032,7129,7652,7835,8005,7978,4089,6132,7598,7951,7884,6078,7789,7627,7546,7141,6107, 7847,7519,8080,7087,7985,7890,7795,7605,7130,7415,7035,7864,8006,4090,6655,6119,7837,7 980,4063,7790,7656,8009,7142,6136,7629,7548,8067,6109,7986,7905,7606,7145,7959,7892,78 51,7797,7635,7132,7037,7838,7743,4092,7609,7419,7095,8010,6123,7630,7535,8096,6110,790 6,6015,8069,7146,7988,7879,7798,7664,7119,8017,7038,7853,7637,4079,7610,7963,7896,7801, 7583,7421,7153,8012,7859,6125,7099,8070,7975,7908,7651,7148,8018,7854,6131,7638,8073,7 543,7992,7883,7802,7612,7965,7422,7154,7775,7641,6126,7127,7861,4087,7101,8128,6911,80 33,7653,8074,8020,7979,7912,6133,7599,7966,7885,6079,7804,7642,7547,7156,7862,8081,710 2,7891,8034,7131,7654,7865,8007,4091,6134,8076,7981,7886,7791,7657,8024,7143,6137,7644, 7549,8082,7987,7920,7607,7160,7893,7866,8036,7133,7839,7982,4093,7658,8011,6138,7631,7 550,8097,6111,7907,8084,7147,7989,7894,7799,7665,7134,7039,7868,4094,7611,7897,8040,76 60,8013,8098,6140,8071,7990,7909,7666,7149,8019,7855,7639,8088,7993,7898,7803,7613,742 3,7155,8014,6127,8100,7910,8129,7150,8048,7668,8075,8021,7994,7913,7614,7967,7900,7805, 7643,7157,7863,7103,8130,8035,7655,8104,8022,7914,6135,8077,7996,7887,7806,7672,8025,7 158,7645,8083,7921,7161,8132,7867,8037,8078,7983,7916,7659,8026,6139,7646,7551,8112,79 22,8085,7162,7895,8038,7135,7869,4095,8136,8041,7661,8028,8099,6141,8086,7991,7924,766 7,7164,7870,8089,7899,8042,7662,8015,6142,8101,7911,8144,7151,8049,7669,8090,7995,7928, 7615,7901,8044,8102,8131,8050,7670,8105,8023,7915,8092,7997,7902,7807,7673,7159,8160,8 133,8106,8052,8079,7998,7917,7674,8027,7647,8113,7923,7163,8134,8039,8108,7918,8137,80 56,7676,8029,8114,8087,7925,7165,7871,8138,8043,7663,8030,6143,8116,7926,8145,7166,809 1,7929,8140,8045,8103,8146,8051,7671,8120,7930,8093,7903,8046,8161,8148,8107,8053,8094, 7999,7932,7675,8162,8135,8054,8109,7919,8152,8057,7677,8115,8164,8110,8139,8058,7678,8 031,8117,7927,7167,8168,8141,8060,8118,8147,8121,7931,8142,8047,8176,8149,8122,8095,79 33,8163,8150,8055,8124,7934,8153,8165,8111,8154,8059,7679,8166,8169,8156,8061,8119,817 0,8143,8062,8177,8123,8172,8178,8151,8125,7935,8180,8126,8155,8167,8184,8157,8171,8158, 8063,8173,8179,8174,8181,8127,8182,8185,8186,8159,8188,8175,8183,8187,8189,8190,8191,],
• wherein when the mother code length is 4096, the first sequence is the sequence Q1, and wherein when the mother code length N is 4096, a quantity K of the K bits is 452, 536, 904, 1048, 1808, 2072, 2712, or 3096;
• and
• transmit the encoded bits over a wireless network.

A non-transitory machine-readable storage medium having instructions stored therein, which when executed by a processor, cause the processor to:

• obtain K bits to be encoded;
• select K sequence numbers from a first sequence, wherein the K bits are placed on polar channels corresponding to the K sequence numbers;
• perform polar code encoding on the K bits to obtain encoded bits, wherein the first sequence comprises sequence numbers of N polar channels, the first sequence is one of Q1, Q2, a sub-sequence Q1 or a sub-sequence Q2, K is a positive integer, N is a mother code length of polar code, N=2n, n is a positive integer, and K≤N, wherein the encoded polar code is utilized to improve performance and to reduce complexity;
• transmit a signal comprising the encoded data bits,
• wherein sequence Q1=[0,1,2,4,8,16,3,32,5,6,9,64,10,17,12,18,128,33,20,34,7,24,36,65,11,256,66,40,13,19,68,14,129,4 8,21,72,130,35,22,25,512,132,37,80,26,38,257,67,136,41,28,258,96,69,42,15,144,49,260,70,44,7 3,131,50,23,1024,264,74,160,513,133,52,81,27,76,514,134,39,272,82,137,56,29,516,259,192,97, 138,84,43,30,145,288,98,261,71,520,140,45,88,146,51,262,100,1025,46,265,75,2048,161,528,14 8,53,320,1026,266,104,77,162,515,135,54,273,83,152,57,1028,268,78,544,164,517,274,193,112, 139,85,58,31,1032,518,384,289,194,99,276,168,86,521,141,60,89,147,290,576,263,196,101,522, 142,1040,47,280,90,2049,176,529,149,292,102,321,1027,524,267,200,105,2050,92,163,530,150, 55,322,1056,153,296,1029,106,269,79,640,545,2052,165,532,275,208,113,154,324,59,1030,270, 108,546,1033,166,519,385,304,195,114,2056,277,169,87,536,156,61,1088,328,1034,548,386,29 1,224,577,278,197,170,116,523,143,1041,62,281,91,2064,177,1036,768,578,388,293,198,103,55 2,336,172,1042,525,282,201,120,2051,93,178,531,151,294,580,323,1152,1057,526,392,297,202, 1044,107,284,2080,94,641,560,2053,180,533,209,352,1058,155,325,298,1031,584,271,204,109, 642,547,2054,1048,167,534,400,305,210,115,2057,184,326,537,1060,157,300,1089,110,329,103 5,644,549,387,2112,306,225,592,2058,279,212,171,117,538,158,1280,63,1090,330,1064,2065,5 50,416,1037,769,226,579,389,308,199,648,118,553,2060,337,173,1043,540,283,216,121,1092,2 066,332,179,1038,770,608,390,295,228,581,554,338,1153,174,1072,527,393,312,203,1045,122, 2176,285,2081,95,656,561,2068,181,1096,772,582,448,353,1154,1059,556,394,340,299,232,104 6,585,286,205,2082,124,643,562,2055,1049,182,535,401,211,354,2072,1536,185,327,1156,776, 1061,586,396,301,206,1104,111,672,344,2084,1050,645,564,402,2113,307,240,593,2059,213,18 6,356,539,1062,159,1281,302,1091,588,331,1160,1065,646,2304,551,417,2114,1052,784,227,59 4,404,2088,309,214,649,119,568,2061,188,1282,541,1120,217,360,1093,1066,2067,333,418,103 9,771,704,609,391,2116,310,229,650,596,555,2062,339,1168,175,1073,542,408,313,218,1284,1 23,1094,2177,2096,334,657,1068,800,2069,610,420,1097,773,230,583,449,368,1155,652,1074,5 57,395,2120,341,314,233,1047,600,2178,287,220,2083,125,658,563,2070,1288,183,1098,774,61 2,450,355,1184,2073,1537,558,424,342,1157,777,234,1076,587,397,316,207,2560,1105,126,673, 2180,345,2085,1051,660,565,403,2128,241,1100,832,2074,1538,452,187,357,1158,778,1063,61 6,398,1296,303,236,1106,589,674,346,1161,2086,1080,647,2305,566,432,2115,1053,785,242,21 84,595,405,2089,215,664,358,569,2076,1540,189,1283,1216,780,1121,590,456,361,1162,1108,1 067,676,2306,348,419,2144,1054,786,705,624,406,2117,2090,311,244,651,597,570,2063,1169,1 90,1312,543,409,1122,219,1285,362,1095,2192,1544,2097,335,1164,896,1069,801,706,2308,61 1,421,2118,1112,788,231,680,598,464,2092,369,1170,653,1075,572,410,2121,315,248,1286,601, 1124,2179,221,2098,364,659,1070,802,2071,1289,422,1099,775,708,613,451,3072,370,1185,65 4,2312,1552,559,425,2122,343,1172,792,235,1077,602,412,2208,317,222,2561,1344,127,688,21 81,2100,1290,661,1128,804,2129,614,480,1101,833,1186,2075,1539,453,426,372,1159,779,712, 1078,617,399,2124,1297,318,237,2562,1107,604,675,2182,347,1176,2087,1081,662,2320,567,4 33,2130,1292,243,1102,2185,834,2104,1568,454,665,359,1188,808,2077,1541,618,428,1298,12 17,781,238,1136,591,457,376,1163,2564,1109,1082,677,2307,2240,349,434,2145,1055,787,720, 2186,625,407,2132,2091,245,666,836,571,2078,1542,1408,191,1313,1218,782,1123,620,458,13 00,363,1192,1110,2193,1545,678,2336,350,1165,897,2146,1084,816,707,2309,626,436,2119,25 68,1113,789,246,681,2188,599,465,2093,1171,668,1314,573,411,2136,1600,249,1287,1220,840, 1125,2194,1546,460,2099,365,1166,898,1071,803,736,2310,1304,423,2148,1114,790,709,682,6 28,466,3073,2094,371,1200,655,2313,1553,574,440,2123,1173,793,250,1316,603,413,1126,220 9,223,2576,1345,366,689,2196,1548,2101,1291,1224,900,1129,805,710,2368,615,481,3074,111 6,848,1187,684,2314,1554,468,427,2152,373,1174,794,713,1079,632,414,2125,2210,319,252,25 63,1346,605,690,2183,1177,2102,1320,663,2321,1130,806,2131,1293,482,1103,2200,835,1664, 2105,1569,455,3076,904,374,1189,809,714,2316,1556,619,429,2126,1299,1232,796,239,2592,1 137,606,472,2212,377,1178,2565,1348,1083,692,2322,2241,435,2160,1294,721,1132,2187,864, 2133,2106,1570,484,667,837,1190,810,2079,1543,1409,430,1328,1219,783,716,1138,621,459,3 080,1301,378,1193,2566,1111,2432,1560,679,2337,2242,351,1180,912,2147,1085,817,722,2324, 2216,627,437,2134,2569,1352,247,696,2189,838,2108,1572,1410,669,1315,1248,812,2137,160 1,622,488,1302,1221,841,1194,1140,2195,1547,461,2338,380,1167,899,2624,1086,818,737,231 1,2244,1305,438,2149,2570,1115,791,724,683,2190,629,467,3088,2095,1201,670,2328,1792,57 5,441,2138,1602,1412,251,1317,1222,842,1127,2224,1576,462,2577,1360,367,1196,928,2197,1 549,738,2340,1306,1225,901,2150,1144,820,711,2369,630,496,3075,2572,1117,849,1202,685,2 315,2248,1555,469,442,2153,1175,795,728,1318,633,415,2140,1604,2211,253,2578,1347,844,6 91,2198,1550,1416,2103,1321,1226,902,1131,807,740,2370,1308,483,3104,1118,2201,850,1665, 686,2344,1584,470,3077,905,2154,375,1204,824,715,2317,1557,634,444,2127,2688,1233,797,2 54,2593,1376,607,473,2213,1179,2580,1349,1322,693,2323,2256,1608,2161,1295,1228,960,113 3,2202,865,1666,2372,2107,1571,485,3078,906,852,1191,811,744,2318,1558,1424,431,2156,13 29,1234,798,717,2594,1139,636,474,3081,2214,379,1208,2567,1350,2433,1561,694,2352,2243, 1181,913,2162,1324,723,2325,1134,2217,866,2135,2584,1353,486,697,2204,839,1668,2109,157 3,1411,3136,908,1330,1249,813,718,2376,1616,623,489,3082,1303,1236,856,1195,2596,1141,2 434,1562,476,2339,2272,381,1182,914,2625,1087,819,752,2326,2245,2218,439,2164,2571,1354, 725,698,2191,868,3089,2110,1574,1440,671,2329,1793,1250,814,2139,1603,1413,490,1332,12 23,843,1672,1142,2225,1577,463,3084,2816,1361,382,1197,929,2626,2436,1564,739,2341,2246, 1307,1240,916,2151,2600,1145,821,726,2384,2220,631,497,3090,2573,1356,1203,700,2330,22 49,1794,443,2168,1632,1414,729,1319,1252,872,2141,1605,2226,1578,492,2579,1362,845,1198, 930,2199,1551,1417,2342,1336,1227,903,2628,1146,822,741,2371,3200,1309,498,3105,2574,1 119,2440,851,1680,687,2345,2250,1585,471,3092,920,2155,1205,825,730,2332,1796,635,445,2 142,1606,2689,1472,255,2608,1377,846,2228,1580,1418,2581,1364,1323,1256,932,2257,1609,7 42,2400,1310,1229,961,3106,1148,2203,880,1667,2373,2346,1586,500,3079,907,2632,853,1206, 826,745,2319,2252,1559,1425,446,2157,2690,1235,799,732,2595,1378,637,475,3096,2215,120 9,2582,1351,2448,1800,695,2353,2258,1610,1420,2163,1325,1230,962,1135,2232,867,1696,237 4,2585,1368,487,3108,936,2205,854,1669,746,2348,1588,1426,3137,909,2158,1331,1264,828,7 19,2377,1617,638,504,3083,2692,1237,857,1210,2597,1380,2435,1563,477,2354,2273,1183,915, 2640,1326,753,2327,2260,1612,2219,2165,2586,1355,964,699,2206,869,1670,3328,2111,1575, 1441,3138,910,1808,1251,815,748,2378,1618,1428,491,3112,1333,1238,858,1673,2598,1143,24 64,1592,478,3085,2817,2274,383,1212,944,2627,2437,1565,754,2356,2247,2696,1241,917,2166, 2601,1384,727,2385,2221,870,3091,2588,1357,1442,701,2331,2264,1795,1728,2169,1633,1415, 3140,968,1334,1253,873,1674,2380,1620,2227,1579,493,3086,2818,1363,860,1199,931,2656,2 438,1566,1432,2343,2276,1337,1242,918,2629,2602,1147,823,756,2386,3201,2222,499,3120,25 75,1358,2441,1681,702,2360,2251,1824,3093,921,2170,1634,1444,731,2333,1797,1254,874,214 3,1607,2704,1473,494,2609,1392,847,1676,2229,1581,1419,3144,2820,1365,1338,1257,933,263 0,2496,1624,743,2401,3202,1311,1244,976,3107,2604,1149,2442,881,1682,2388,2347,2280,158 7,501,3094,922,2633,1207,827,760,2334,2253,1798,447,2172,1636,2691,1474,733,2610,1379,8 76,3097,2230,1582,1448,2583,1366,2449,1801,1258,934,2259,1611,1421,2402,1340,1231,963,3 584,1150,2233,882,1697,2375,3204,2824,1369,502,3109,937,2634,2444,855,1684,747,2349,225 4,1589,1427,3152,924,2159,2720,1265,829,734,2392,1856,639,505,3098,2693,1476,1211,2612, 1381,2450,1802,2355,2288,1640,1422,2641,1327,1260,992,2261,1613,2234,1698,2404,2587,13 70,965,3110,938,2207,884,1671,3329,2350,1590,1456,3139,911,2636,1809,1266,830,749,2379, 3208,1619,1429,506,3113,2694,1239,859,1688,2599,1382,2465,1593,479,3100,2832,2275,1213, 945,2642,2452,1804,755,2357,2262,1614,2697,1480,2167,2616,1385,966,2236,871,1700,3330,2 589,1372,1443,3168,940,2265,1810,1729,750,2408,1648,1430,3141,969,3114,1335,1268,888,16 75,2381,1621,2466,1594,508,3087,2819,2752,861,1214,946,2657,2439,1567,1433,2358,2277,26 98,1243,919,2644,2603,1386,757,2387,3216,2223,3121,2590,1359,2456,1920,703,2361,2266,18 25,1730,3332,2171,1635,1445,3142,970,1812,1255,875,1704,2382,1622,2705,1488,495,3116,28 48,1393,862,1677,2658,2468,1596,1434,3145,2821,2278,1339,1272,948,2631,2497,1625,758,24 16,3203,2700,1245,977,3122,2605,1388,2443,1683,2389,2362,2281,1826,3095,923,2648,1446,7 61,2335,2268,1799,1732,2173,1637,2706,1475,972,2611,1394,877,1678,3336,2231,1583,1449,3 146,2822,1367,1816,1259,935,2660,2498,1626,1436,2403,3232,1341,1246,978,3585,2606,1151, 2472,883,1712,2390,3205,2825,2282,503,3124,952,2635,2445,1685,762,2364,2255,1828,3153,9 25,2174,1638,2721,1504,735,2393,1857,878,3099,2708,1477,1450,2613,1396,2451,1803,1736,2 289,1641,1423,3148,2880,1342,1261,993,3586,2500,1628,2235,1699,2405,3206,2826,1371,980, 3111,939,2664,2446,885,1686,3344,2351,2284,1591,1457,3154,926,2637,2722,1267,831,764,23 94,3209,1858,507,3128,2695,1478,1689,2614,1383,2480,1832,3101,2833,2290,1642,1452,2643, 2453,1805,1262,994,2263,1615,2712,1481,2406,2617,1400,967,3588,2237,886,1701,3331,3264, 2828,1373,1458,3169,941,2638,2504,1811,1744,751,2409,3210,1649,1431,3156,984,3115,2724, 1269,889,1690,2396,1860,2467,1595,509,3102,2834,2753,1215,947,2672,2454,1806,2359,2292, 1644,2699,1482,2645,2618,1387,996,3217,2238,1702,3360,2591,1374,2457,1921,3170,942,226 7,1840,1731,3333,2410,1650,1460,3143,971,3592,1813,1270,890,1705,2383,3212,1623,2944,14 89,510,3 117,2849,2754,863,1692,2659,2469,1597,1435,3160,2836,2279,2728,1273,949,2646,25 12,1864,759,2417,3218,2701,1484,3123,2620,1389,2458,1922,2363,2296,1827,1760,3334,2649, 1447,3172,1000,2269,1814,1733,1706,2412,1652,2707,1490,973,3118,2850,1395,892,1679,333 7,2470,1598,1464,3147,2823,2756,1817,1274,950,2661,2499,1627,1437,2418,3233,2702,1247,9 79,3600,2607,1390,2473,1713,2391,3220,2840,2283,3125,953,2650,2460,1924,763,2365,2270,1 829,1734,3392,2175,1639,2736,1505,974,1872,879,1708,3338,2709,1492,1451,3176,2852,1397, 1818,1737,2662,2528,1656,1438,3149,2881,3234,1343,1276,1008,3587,2501,1629,2474,1714,2 420,3207,2827,2760,981,3126,954,2665,2447,1687,3345,2366,2285,1830,3155,927,2652,2723,1 506,765,2395,3224,1859,3129,2710,1479,1928,2615,1398,2481,1833,1738,3340,2291,1643,145 3,3150,2882,1820,1263,995,3616,2502,1630,2713,1496,2407,3236,2856,1401,982,3589,2666,24 76,887,1716,3346,3265,2829,2286,1459,3184,956,2639,2505,1745,766,2424,3211,1888,3157,98 5,3130,2725,1508,1691,2397,1861,2482,1834,3103,2835,2768,1454,2673,2455,1807,1740,2293, 1645,2714,1483,2884,2619,1402,997,3590,3456,2239,1703,3361,3266,2830,1375,1936,3171,94 3,2668,2506,1841,1746,3348,2411,3240,1651,1461,3158,986,3593,2726,1271,891,1720,2398,32 13,1862,2945,511,3132,2864,2755,1693,2674,2484,1836,3161,2837,2294,1646,2729,1512,2647, 2513,1865,998,3219,2716,1485,3362,2621,1404,2459,1923,3648,2297,1842,1761,3335,3268,28 88,1462,3173,1001,3594,2508,1815,1748,1707,2413,3214,1653,2946,1491,988,3119,2851,2784, 893,1694,3352,2471,1599,1465,3162,2838,2757,2730,1275,951,2676,2514,1866,2419,3248,270 3,1486,3601,2622,1391,2488,1952,3221,2841,2298,1762,3364,2651,2461,1925,3174,1002,2271, 1844,1735,3393,2414,1654,2737,1520,975,3596,1873,894,1709,3339,3272,2948,1493,1466,317 7,2853,2758,1819,1752,2663,2529,1657,1439,3164,2896,3235,2732,1277,1009,3602,2516,1868, 2475,1715,2421,3222,2842,2761,3127,955,2680,2462,1926,2367,2300,1831,1764,3394,2653,27 38,1507,1004,3225,1874,1710,3368,2711,1494,1929,3178,2854,1399,1848,1739,3341,2530,165 8,1468,3151,2883,3712,1821,1278,1010,3617,2503,1631,2952,1497,2422,3237,2857,2762,983,3 604,2667,2477,1717,3347,3280,2844,2287,3185,957,2654,2520,1984,767,2425,3226,1889,3396, 3131,2740,1509,1930,1876,2483,1835,1768,3342,2769,1455,3180,2912,1822,1741,3618,2532,1 660,2715,1498,2885,3238,2858,1403,1012,3591,3457,2478,1718,3376,3267,2831,2764,1937,31 86,958,2669,2507,1747,3349,2426,3241,1890,3159,987,3608,2727,1510,1721,2399,3228,1863,2 960,3133,2865,2770,1932,2675,2485,1837,1742,3400,2295,1647,2744,1513,2886,1880,999,362 0,3458,2717,1500,3363,3296,2860,1405,1938,3649,2670,2536,1843,1776,3350,3269,2889,3242, 1463,3188,1016,3595,2509,1749,1722,2428,3215,1892,2947,989,3134,2866,2785,1695,3353,24 86,1838,3163,2839,2772,2731,1514,2677,2515,1867,3249,2718,1487,3840,2623,1406,2489,195 3,3650,3460,2299,1763,3365,3270,2890,1940,3175,1003,3624,2510,1845,1750,3408,2415,3244, 1655,2976,1521,990,3597,2786,895,1724,3354,3273,2949,1467,3192,2868,2759,1753,2678,254 4,1896,3165,2897,3250,2733,1516,3603,2517,1869,2490,1954,3223,2843,2776,3366,2681,2463, 1927,3652,2301,1846,1765,3395,2892,2739,1522,1005,3598,3464,1875,1711,3369,3274,2950,1 495,1944,3179,2855,2788,1849,1754,3356,2531,1659,1469,3166,2898,3713,2734,1279,1011,36 32,2518,1870,2953,2423,3252,2872,2763,3605,2682,2492,1956,3281,2845,2302,1766,3424,265 5,2521,1985,1006,3227,1904,3397,3370,2741,1524,1931,3656,1877,1850,1769,3343,3276,3008, 1470,3181,2913,3714,1823,1756,3619,2533,1661,2954,1499,2900,3239,2859,2792,1013,3606,3 472,2479,1719,3377,3282,2846,2765,3187,959,2684,2522,1986,2427,3256,1891,3398,3609,274 2,1511,1960,3229,1878,2961,1770,3372,2771,1933,3182,2914,1852,1743,3401,2534,1662,2745, 1528,2887,3716,1881,1014,3621,3459,2956,1501,3378,3297,2861,2766,1939,3664,2671,2537,1 777,3351,3284,2904,3243,3189,1017,3610,2524,1988,1723,2429,3230,1893,2962,3135,2867,28 00,1934,2487,1839,1772,3402,2773,2746,1515,2916,1882,3622,3488,2719,1502,3841,3298,286 2,1407,1968,3651,3461,2538,1778,3380,3271,2891,3720,1941,3190,1018,3625,2511,1751,3409, 2430,3245,1894,2977,991,3612,2787,1725,3355,3288,2964,3193,2869,2774,1992,2679,2545,18 97,3404,3251,2748,1517,3842,1884,2491,1955,3680,3462,2777,3367,3300,2920,1942,3653,362 6,2540,1847,1780,3410,2893,3246,2978,1523,1020,3599,3465,1726,3384,3275,2951,1945,3194, 2870,2789,1755,3357,2546,1898,3167,2899,3728,2735,1518,3633,2519,1871,2968,3253,2873,2 778,3844,2683,2493,1957,3654,3520,2303,1767,3425,2894,2000,1007,3628,3466,1905,3412,33 71,3304,2980,1525,1946,3657,2790,1851,1784,3358,3277,3009,1471,3196,2928,3715,1757,363 4,2548,1900,2955,2901,3254,2874,2793,3607,3473,2494,1958,3283,2847,2780,3426,2685,2523, 1987,3257,1906,3399,3848,2743,1526,1961,3658,3468,1879,1771,3373,3278,3010,1948,3183,2 915,3744,1853,1758,3416,2535,1663,2984,1529,2902,3717,2794,1015,3636,3474,2957,3379,33 12,2876,2767,3665,2686,2552,2016,3285,2905,3258,3428,3611,2525,1989,1962,3231,1908,296 3,3374,2801,1935,3660,1854,1773,3403,3012,2747,1530,2917,3718,1883,3623,3489,2958,1503, 3856,3299,2863,2796,1969,3666,3476,2539,1779,3381,3286,2906,3721,3191,1019,3640,2526,1 990,2431,3260,1895,2992,3613,2802,1964,3289,2965,1774,3432,2775,1993,2918,1912,3405,34 90,2749,1532,3843,3776,1885,1970,3681,3463,3016,3382,3301,2921,3722,1943,3668,3627,254 1,1781,3411,2908,3247,2979,1021,3614,3480,1727,3385,3290,2966,3195,2871,2804,1994,2547, 1899,3406,3729,2750,1519,3872,1886,2969,3682,3492,2779,3845,3302,2922,1972,3655,3521,2 542,1782,3440,2895,3724,2001,1022,3629,3467,3413,3386,3305,2981,1947,3672,2791,1785,33 59,3292,3024,3197,2929,3730,1996,3635,2549,1901,2970,3255,2875,2808,3846,2495,1959,368 4,3522,2781,3427,2924,2002,3630,3496,1907,3414,3849,3306,2982,1527,1976,3659,3469,1786, 3388,3279,3011,1949,3198,2930,3745,1759,3417,2550,1902,2985,2903,3732,2795,3637,3475,2 972,3313,2877,2782,3904,2687,2553,2017,3524,3259,3429,3850,2004,1963,3688,3470,1909,33 75,3308,3040,1950,3661,3746,1855,1788,3418,3013,2986,1531,2932,3719,3638,3504,2959,385 7,3314,2878,2797,3667,3477,2554,2018,3287,2907,3736,3430,3641,2527,1991,3261,1910,2993, 3852,2803,1965,3662,3528,1775,3433,3014,2008,2919,3748,1913,3420,3491,2988,1533,3858,3 777,2798,1971,3696,3478,3017,3383,3316,2936,3723,3669,3642,2556,2020,2909,3262,2994,36 15,3481,1966,3291,2967,3434,2805,1995,1914,3407,3968,2751,1534,3873,3778,1887,3683,349 3,3018,3860,3303,2923,3752,1973,3670,3536,2543,1783,3441,2910,3725,1023,3644,3482,3387, 3320,2996,3673,2806,2024,3293,3025,3436,3731,1997,3874,1916,2971,3494,2809,3847,3780,1 974,3685,3523,3020,3442,2925,3726,2003,3631,3497,3415,3864,3307,2983,1977,3674,3484,17 87,3389,3294,3026,3199,2931,3760,1998,2551,1903,3000,3733,2810,3876,2973,3686,3552,278 3,3905,2926,2032,3525,3498,3444,3851,3784,2005,1978,3689,3471,3390,3309,3041,1951,3676, 3747,1789,3419,3028,2987,2933,3734,3639,3505,2974,3315,2879,2812,3906,2555,2019,3526,3 737,3431,3880,2006,3690,3500,1911,3853,3310,3042,1980,3663,3529,1790,3448,3015,2009,29 34,3749,3421,3506,2989,3859,3792,2799,3697,3479,3032,3317,2937,3738,3908,3643,2557,202 1,3263,2995,3854,1967,3692,3530,3435,3044,2010,3750,1915,3422,3969,2990,1535,3888,3779, 3698,3508,3019,3861,3318,2938,3753,3671,3537,2558,2022,2911,3740,3645,3483,3321,2997,3 912,2807,2025,3532,3437,3970,2012,3875,3808,1917,3495,3048,3862,3781,3754,1975,3700,35 38,3021,3443,2940,3727,3646,3512,3865,3322,2998,3675,3485,2026,3295,3027,3438,3761,199 9,1918,3001,3972,2811,3877,3782,3687,3553,3022,3920,2927,3756,2033,3540,3499,3445,3866, 3785,1979,3704,3486,3391,3324,3056,3677,3762,2028,3029,3002,3735,3878,2975,3554,2813,3 907,2034,3527,3976,3446,3881,3786,2007,3691,3501,3868,3311,3043,1981,3678,3544,1791,34 49,3030,2935,3764,3507,3004,3793,2814,3936,3033,3556,3739,3909,3882,2036,3502,3855,378 8,1982,3693,3531,3450,3045,2011,3751,3423,3984,2991,3889,3794,3699,3509,3034,3319,2939, 3768,3910,2559,2023,3741,3884,3694,3560,3913,3046,2040,3533,3452,3971,2013,3890,3809,3 510,3049,3863,3796,3755,3701,3539,3036,2941,3742,3647,3513,3323,2999,3914,2027,3534,34 39,4000,2014,3810,1919,3973,3050,3892,3783,3702,3568,3023,3921,2942,3757,3541,3514,386 7,3800,3705,3487,3325,3057,3916,3763,2029,3003,3974,3879,3812,3555,3052,3922,3758,2035, 3542,3977,3447,3896,3787,3706,3516,3869,3326,3058,3679,3545,2030,3031,3765,3005,4032,2 815,3937,3557,3978,3924,3883,3816,2037,3503,3870,3789,1983,3708,3546,3451,3060,3766,39 85,3006,3795,3938,3035,3558,3769,3911,2038,3980,3885,3790,3695,3561,3928,3047,2041,354 8,3453,3986,3891,3824,3511,3064,3797,3770,3940,3037,3743,3886,3562,3915,2042,3535,3454, 4001,2015,3811,3988,3051,3893,3798,3703,3569,3038,2943,3772,3515,3801,3944,3564,3917,4 002,2044,3975,3894,3813,3570,3053,3923,3759,3543,3992,3897,3802,3707,3517,3327,3059,39 18,2031,4004,3814,4033,3054,3952,3572,3979,3925,3898,3817,3518,3871,3804,3709,3547,306 1,3767,3007,4034,3939,3559,4008,3926,3818,2039,3981,3900,3791,3710,3576,3929,3062,3549, 3987,3825,3065,4036,3771,3941,3982,3887,3820,3563,3930,2043,3550,3455,4016,3826,3989,3 066,3799,3942,3039,3773,4040,3945,3565,3932,4003,2045,3990,3895,3828,3571,3068,3774,39 93,3803,3946,3566,3919,2046,4005,3815,4048,3055,3953,3573,3994,3899,3832,3519,3805,394 8,4006,4035,3954,3574,4009,3927,3819,3996,3901,3806,3711,3577,3063,4064,4037,4010,3956, 3983,3902,3821,3578,3931,3551,4017,3827,3067,4038,3943,4012,3822,4041,3960,3580,3933,4 018,3991,3829,3069,3775,4042,3947,3567,3934,2047,4020,3830,4049,3070,3995,3833,4044,39 49,4007,4050,3955,3575,4024,3834,3997,3807,3950,4065,4052,4011,3957,3998,3903,3836,357 9,4066,4039,3958,4013,3823,4056,3961,3581,4019,4068,4014,4043,3962,3582,3935,4021,3831, 3071,4072,4045,3964,4022,4051,4025,3835,4046,3951,4080,4053,4026,3999,3837,4067,4054,3 959,4028,3838,4057,4069,4015,4058,3963,3583,4070,4073,4060,3965,4023,4074,4047,3966,40 81,4027,4076,4082,4055,4029,3839,4084,4030,4059,4071,4088,4061,4075,4062,3967,4077,408 3,4078,4085,4031,4086,4089,4090,4063,4092,4079,4087,4091,4093,4094,4095,],
• wherein sequence Q2=[6309,5445,6419,5391,6298,6203,5667,5287,6414,5654,6252,5425,5330,5235,6310,6663,5446, 5657,6339,5277,3623,6258,5420,4819,6421,5230,6313,6231,5449,3381,3721,6300,4935,6205,5 669,5507,5004,5426,5345,4909,4814,3613,3289,5399,5332,5291,6692,5237,5658,6435,5278,34 05,5010,5183,4915,6422,6341,6314,3681,6260,3463,6667,5450,4821,3382,3301,4794,3722,628 7,4964,3668,3627,6206,5670,3411,4767,6425,3247,2979,5346,4910,3614,6235,3480,5699,5509, 4586,3385,3290,5428,2966,5319,4939,5768,3195,5238,6321,5673,4559,7180,5457,4478,5293,3 406,5025,6722,3729,6532,5660,4835,6437,6342,5403,2969,5336,5012,3682,6247,3492,6696,52 41,2779,4917,4822,3845,6480,3302,2922,6316,4727,4593,3655,7186,3521,6669,5452,5299,344 0,4796,2895,6426,3724,6345,4539,3629,6264,3467,5728,5510,3413,4825,3386,3305,5415,2981, 5348,4968,1947,3672,6237,5701,2791,6322,5674,4588,3359,3292,6675,5458,4941,5294,3197,5 026,2929,3730,6295,5647,5513,3635,6438,2549,1901,5432,2970,5323,4999,6724,3255,2875,52 42,4918,4837,3846,6467,5405,2495,1959,4594,3684,7201,3522,6670,5215,2781,6536,4947,577 6,3427,4783,2924,6441,6346,5681,2002,4567,7188,5016,3630,6251,3496,1907,5301,3414,4921, 4826,3849,6428,3306,5892,2982,1527,4731,1976,4541,3659,6238,3469,5702,6785,5568,1786,4 351,3388,3279,6704,5473,3011,4942,1949,3198,2930,3745,6324,5676,1759,5514,3417,6677,54 60,2550,1902,5419,2985,5352,5028,2903,3732,6353,5705,2795,4838,3637,6496,3475,5406,297 2,5325,5057,7202,3313,2877,5244,2782,6299,4976,5763,6469,2687,6442,2553,5682,2017,4596, 7175,3524,5003,6728,3259,4949,5302,3429,4922,4841,3850,6415,6348,5655,2004,5521,1963,4 542,3688,6253,3470,1909,6786,5331,4895,4828,3375,3308,6691,5474,3040,4733,1950,4571,36 61,7192,3746,6311,1855,1788,5305,3418,6678,5447,3013,6544,5896,2986,1531,4791,2932,644 9,3719,6354,5706,5516,3638,6259,3504,5421,2959,5326,5058,3857,3314,2878,5231,2797,6328, 4963,5792,3667,6470,3477,6681,5464,2554,2018,4583,7204,3287,5032,2907,3736,6301,4950,5 765,3430,4842,3641,6444,2527,5684,1991,5522,7233,5005,6254,3261,1910,5427,2993,5360,49 24,4815,3852,6473,5713,2803,4734,1965,4600,3662,7179,3528,6788,5333,4953,1775,5306,343 3,6693,5476,3014,6531,5659,2008,4573,2919,6450,3748,6369,1913,5279,3420,5011,6736,3491, 5422,2988,1533,4849,3858,6423,3777,6356,5708,2798,6315,1971,3696,6261,3478,6682,5451,3 017,5060,3383,3316,4795,2936,3723,6302,4965,5766,3669,3642,6207,2556,5671,2020,5537,72 34,5006,2909,3262,5904,2994,5347,4911,4844,3615,6474,3481,5714,5524,1966,4587,7208,329 1,5429,2967,5334,4954,5769,3434,6694,5239,2805,6560,5688,1995,4574,7181,6913,6370,1914, 4479,5308,3407,5040,6723,3968,6533,5661,2751,1534,4850,3873,6452,3778,6343,1887,6792,5 337,5013,3683,6262,3493,6697,5480,3018,4823,3860,6481,3303,2923,3752,6317,4966,1973,36 70,7187,3536,6684,5453,2543,1783,5538,3441,4797,2910,6427,3725,6360,5891,5824,1023,364 4,6265,3482,5729,5511,7236,5064,3387,3320,5430,2996,5349,4969,5770,3673,6476,5716,2806, 6323,5675,2024,4589,7182,3293,6914,5459,3025,4956,5295,3436,5027,6752,3731,6534,5662,1 997,5528,3874,6439,6372,1916,5433,2971,5338,5014,6725,3494,6698,5243,2809,4919,4852,38 47,6482,3780,7297,6318,1974,4595,3685,7216,3523,6671,5454,3020,6537,5777,3442,4798,292 5,6456,3726,6347,5920,2003,7189,5017,3631,6266,3497,5730,5540,3415,4827,3864,6429,3307, 5893,2983,5350,4970,1977,3674,6239,3484,5703,6800,5569,1787,4590,3389,3294,6705,5488,3 026,4943,5772,3199,2931,3760,6325,5677,1998,5515,7240,6916,5461,2551,1903,5434,3000,53 53,5029,6726,3733,6592,5720,2810,4839,3876,6497,7298,5407,2973,5340,5072,3686,7203,355 2,6700,5245,2783,6538,4977,5778,3905,6484,2926,6443,6376,5683,2032,4597,7190,3525,5018, 6729,3498,5303,3444,4923,4856,3851,6430,3784,6349,5894,2005,1978,4543,3689,6268,3471,5 732,6787,5570,4829,3390,3309,6706,5475,3041,4972,1951,3676,7193,3747,6326,5678,1789,55 44,3419,6679,5462,3028,6545,5897,2987,5354,5030,2933,3734,6355,5707,5517,3639,6498,350 5,5436,2974,5327,5059,3315,2879,5246,2812,6329,4978,5793,3906,6471,7300,6920,5465,2555, 2019,4598,7205,3526,5033,6730,3737,6540,4951,5780,3431,4843,3880,6350,5685,2006,5523,7 248,5020,3690,6255,3500,1911,6816,5361,4925,4830,3853,6488,3310,5952,3042,4735,1980,46 01,3663,7194,3529,6789,5572,1790,5307,3448,6708,5477,3015,6546,5898,2009,2934,3749,638 4,5736,5518,3421,3506,5423,2989,5356,5088,3859,3792,2799,5794,3697,6500,3479,5466,3032, 5061,3317,5034,2937,3738,4980,3908,7425,3643,2557,2021,5552,5007,3263,5905,2995,5362,4 926,4845,3854,7304,1967,4602,3692,3530,5335,4955,5784,3435,3044,2010,4575,6928,3750,19 15,5309,3422,5041,3969,5900,2990,1535,4851,3888,3779,5576,3698,3508,3019,5062,3318,293 8,4967,7426,3537,2558,2022,7264,5036,2911,3740,4846,3645,3483,5744,3321,2997,4984,3912, 2807,2025,4604,3532,6848,3437,3970,2012,3808,1917,3048,7312,1975,3021,6016,2940,7428,3 512,2998,2026,6944,1918,3972,3920,3056,7681,6445,6451,6737,6357,5709,6330,6683,7206,63 03,5767,6446,5686,7235,6732,6475,5715,5525,7209,6790,6695,5478,6561,5689,7196,6371,673 8,6548,6453,6358,5710,6793,6263,6712,5481,3861,3753,6332,5796,3671,6685,5468,5539,6361, 5906,5825,6504,5526,7237,5065,7210,5431,5364,5771,6477,5717,6562,5690,7183,6915,4957,5 310,5042,6753,6535,5663,5529,3875,6454,6373,6794,5339,5015,6740,3495,6699,5482,4853,38 62,6483,3781,3754,6319,3700,7217,3538,6686,5455,6552,3443,4799,6457,3727,6362,5921,582 6,3646,6267,5731,5541,7238,5066,3865,3322,5908,5351,4971,5800,3675,6478,3485,5718,6801, 5584,4591,7212,3295,5489,3027,4958,5773,3438,6754,3761,6564,5692,1999,5530,7241,6917,6 374,5435,3001,5368,5044,6727,6593,5721,2811,4854,3877,6512,3782,7299,6796,5341,5073,36 87,7218,3553,6701,5484,3022,6539,5779,6485,2927,6458,3756,6377,5922,2033,7191,3540,501 9,6744,3499,5542,3445,4857,3866,6431,3785,6364,5895,5828,1979,3704,6269,3486,5733,6802, 5571,5068,3391,3324,6707,5490,4973,5774,3677,7432,3762,6327,5679,2028,5545,7242,6918,5 463,3029,5912,3002,5355,5031,6756,3735,6594,5722,5532,3878,6499,7328,5437,2975,5342,50 74,3554,6702,5247,2813,6568,4979,5808,3907,6486,7301,6921,6378,2034,4599,7220,3527,504 8,6731,3976,6541,5781,3446,4858,3881,6460,3786,6351,5924,2007,7249,5021,3691,6270,3501, 5734,6817,5600,4831,3868,6489,3311,5953,3043,4974,1981,3678,7195,3544,6804,5573,1791,5 546,3449,6709,5492,3030,6547,5899,5832,2935,3764,6385,5737,5519,7244,6976,3507,5438,30 04,5357,5089,7682,3793,6596,5724,2814,6331,5795,3936,6501,7302,6922,5467,3033,5076,720 7,3556,5035,6760,3739,6542,4981,5782,3909,7440,3882,6447,6380,5687,2036,5553,7250,5022, 6733,3502,6818,5363,4927,4860,3855,6490,3788,7305,5954,1982,4603,3693,7224,3531,6791,5 574,5785,3450,6710,5479,3045,6576,5928,2011,7197,6929,3751,6386,5738,5548,3423,6739,39 84,6549,5901,2991,5358,5090,3889,3794,6359,5711,6808,5577,3699,6502,3509,6713,5496,303 4,5063,7684,3319,2939,3768,6333,4982,5797,3910,7427,7360,6924,5469,2559,2023,5554,7265, 5037,6734,3741,6600,5907,5840,4847,3884,6505,7306,5745,5527,7252,5080,3694,7211,3560,6 820,5365,4985,5786,3913,6492,5956,3046,6563,5691,2040,4605,7198,3533,6930,6849,5311,34 52,5043,6768,3971,6550,5902,2013,3890,6455,3809,6388,5740,6795,5578,6741,3510,6714,548 3,3049,5092,3863,3796,7313,3755,6334,5798,3701,7456,3539,6687,5470,3036,6553,6017,7266, 5038,2941,3742,6363,5936,5827,7429,3647,6506,3513,5746,5556,7239,5067,7688,3323,5909,2 999,5366,4986,5801,3914,6479,7308,5719,7040,5585,2027,4606,7213,3534,6945,6850,4959,57 88,3439,6755,4000,6565,5693,2014,5531,7256,6932,3810,6375,1919,6824,5369,5045,6742,397 3,6608,5960,3050,4855,3892,6513,3783,7314,6797,5580,3702,7219,3568,6716,5485,3023,6554, 6018,3921,2942,6459,3757,6392,5923,5856,7430,3541,6745,3514,5543,7268,5096,3867,3800,6 365,5910,5829,5802,3705,6508,3487,5748,6803,5586,5069,7214,3325,6946,5491,3057,4988,57 75,3916,7433,3763,6566,5694,2029,5560,7243,6919,6852,5913,3003,5370,5046,6757,3974,659 5,5723,5533,3879,6514,3812,7329,6798,5343,5075,7696,3555,6703,5486,3052,6569,5809,3922, 6487,7316,6936,3758,6379,2035,7221,3542,5049,6746,3977,6556,6020,3447,4859,3896,6461,3 787,6366,5925,5830,7488,3706,6271,3516,5735,6832,5601,5070,3869,3326,5968,3058,4975,58 04,3679,7434,3545,6805,5588,2030,5547,7272,6948,5493,3031,5914,5833,6758,3765,6624,575 2,5534,7245,6977,7330,5439,3005,5372,5104,7683,4032,6597,5725,2815,6570,5810,3937,6516, 7303,6923,6856,5077,7222,3557,5050,6761,3978,6543,5783,3924,7441,3883,6462,3816,6381,5 926,2037,7251,5023,6748,3503,6819,5602,4861,3870,6491,3789,7320,5955,1983,3708,7225,35 46,6806,5575,6024,3451,6711,5494,3060,6577,5929,5834,7436,3766,6387,5739,5549,7246,697 8,3985,5916,3006,5359,5091,7712,3795,6598,5726,6809,5592,3938,6503,7332,6952,5497,3035, 5078,7685,3558,6762,3769,6572,4983,5812,3911,7442,7361,6925,6382,2038,5555,7280,5052,6 735,3980,6601,5841,4862,3885,6520,3790,7307,5984,7253,5081,3695,7226,3561,6821,5604,57 87,3928,6493,5957,3047,6578,5930,2041,7199,3548,6931,6864,5550,3453,6769,3986,6551,590 3,5836,3891,3824,6389,5741,6810,5579,6980,3511,6715,5498,3064,5093,7686,3797,7552,3770, 6335,5799,3940,7457,7362,6926,5471,3037,6032,7267,5039,6764,3743,6602,5937,5842,7444,3 886,6507,7336,5747,5557,7254,5082,7689,3562,6822,5367,4987,5816,3915,6494,7309,5958,70 41,2042,4607,7228,3535,6960,6851,5789,3454,6770,4001,6580,5932,2015,7257,6933,3811,639 0,5742,6825,5608,6743,3988,6609,5961,3051,5094,3893,3798,7315,6812,5581,3703,7458,3569, 6717,5500,3038,6555,6019,7744,2943,3772,6393,5938,5857,7431,7364,6984,3515,5558,7269,5 097,7690,3801,6604,5911,5844,5803,3944,6509,7310,5749,7042,5587,5084,7215,3564,6947,68 80,4989,5790,3917,7448,4002,6567,5695,2044,5561,7258,6934,6853,6826,5371,5047,6772,397 5,6610,5962,3894,6515,3813,7344,6799,5582,7697,3570,6718,5487,3053,6584,6048,3923,7317, 6937,3759,6394,5858,7460,3543,6747,3992,6557,6021,7270,5098,3897,3802,6367,5940,5831,7 489,3707,6510,3517,5750,6833,5616,5071,7692,3327,5969,3059,4990,5805,3918,7435,7368,70 44,5589,2031,5562,7273,6949,6854,5915,5848,6759,4004,6625,5753,5535,7260,6992,3814,733 1,6828,5373,5105,7698,4033,6612,5964,3054,6571,5811,3952,6517,7318,6938,6857,7223,3572, 5051,6776,3979,6558,6022,3925,3898,6463,3817,6396,5927,5860,7490,6749,3518,6834,5603,5 100,3871,3804,7321,5970,5806,3709,7464,3547,6807,5590,6025,7274,6950,5495,3061,5944,58 35,7437,3767,6626,5754,5564,7247,6979,7808,5917,3007,5374,5106,7713,4034,6599,5727,704 8,5593,3939,6518,7333,6953,6858,5079,7700,3559,6763,4008,6573,5813,3926,7443,7376,6940, 3818,6383,2039,7281,5053,6750,3981,6616,6080,4863,3900,6521,3791,7322,5985,7492,3710,7 227,3576,6836,5605,6026,3929,5972,3062,6579,5931,5864,7438,3549,6865,5551,7276,7008,39 87,5918,5837,7714,3825,6628,5756,6811,5594,6981,7334,6954,5499,3065,5108,7687,4036,755 3,3771,6574,5814,3941,7472,7363,6927,6860,6033,7282,5054,6765,3982,6603,5843,7445,3887, 6522,3820,7337,5986,7255,5083,7704,3563,6823,5606,5817,3930,6495,7324,5959,7056,2043,7 229,3550,6961,6866,6028,3455,6771,4016,6581,5933,5838,7496,3826,6391,5743,6840,5609,69 82,3989,5976,3066,5095,7716,3799,7554,6813,5596,3942,7459,7392,6956,5501,3039,6034,774 5,6766,3773,6632,5939,5872,7446,7365,6985,7338,5559,7284,5112,7691,4040,6605,5845,5818, 3945,6524,7311,5988,7043,5085,7230,3565,6962,6881,5791,3932,7449,4003,6582,5934,2045,7 259,6935,6868,6827,5610,6773,3990,6611,5963,3895,3828,7345,6814,5583,7936,3571,6719,55 02,3068,6585,6049,7746,7556,3774,6395,5859,7461,7366,6986,3993,6036,7271,5099,7720,380 3,6606,5941,5846,7504,3946,6511,7340,5751,7072,5617,5086,7693,3566,6882,4991,5820,3919, 7450,7369,7045,2046,5563,7288,6964,6855,5849,6774,4005,6640,5992,7261,6993,3815,7346,6 829,5612,7699,4048,6613,5965,3055,6586,6050,3953,7319,6939,6872,7462,3573,6777,3994,65 59,6023,7748,3899,3832,6397,5942,5861,7491,6988,3519,6835,5618,5101,7694,3805,7560,597 1,5807,3948,7465,7370,7046,5591,6040,7275,6951,6884,5945,5850,7452,4006,6627,5755,5565, 7262,6994,7809,6830,5375,5107,7728,4035,6614,5966,7049,3954,6519,7348,6968,6859,7701,3 574,6778,4009,6588,6052,3927,7377,6941,3819,6398,5862,7520,6751,3996,6617,6081,5102,39 01,3806,7323,6000,7493,3711,7466,3577,6837,5620,6027,7752,5973,3063,5946,5865,7439,737 2,7104,5566,7277,7009,7810,5919,5852,7715,4064,6629,5757,7050,5595,6996,7335,6955,6888, 5109,7702,4037,7568,4010,6575,5815,3956,7473,7378,6942,6861,7283,5055,6780,3983,6618,6 082,3902,6523,3821,7352,5987,7494,7705,3578,6838,5607,6056,3931,7325,5974,7057,5866,74 68,3551,6867,6029,7278,7010,4017,5948,5839,7497,3827,6630,5758,6841,5624,6983,7812,597 7,3067,5110,7717,4038,7555,7052,5597,3943,7474,7393,6957,6862,6035,7760,6767,4012,6633, 5873,7447,7380,7000,3822,7339,7285,5113,7706,4041,6620,6084,5819,3960,6525,7326,5989,7 058,7231,3580,6963,6896,6030,3933,4018,6583,5935,5868,7498,6869,6842,5611,7012,3991,59 78,7718,3829,7584,6815,5598,7937,7394,6958,5503,3069,6064,7747,7557,3775,6634,5874,747 6,7367,6987,7816,6037,7286,5114,7721,4042,6607,5847,7505,3947,6526,7341,5990,7073,5087, 7708,3567,6883,5821,3934,7451,7384,7060,2047,7289,6965,6870,6088,6775,4020,6641,5993,7 500,3830,7347,6844,5613,7938,4049,5980,3070,6587,6051,7776,7558,6873,7463,7396,7016,39 95,6038,7749,7722,3833,6636,5943,5876,7506,6989,7342,7074,5619,5116,7695,4044,7561,582 2,3949,7480,7371,7047,6041,7290,6966,6885,5851,7453,4007,6642,5994,7263,6995,7824,6831, 5614,7729,4050,6615,5967,7064,3955,7349,6969,6874,7940,3575,6779,4024,6589,6053,7750,7 616,3834,6399,5863,7521,6990,3997,6096,5103,7724,3807,7562,6001,7508,3950,7467,7400,70 76,5621,6042,7753,6886,5947,5880,7454,7373,7105,5567,7292,7024,7811,5853,7730,4065,664 4,5996,7051,6997,7350,6970,6889,7703,4052,7569,4011,6590,6054,3957,7379,6943,6876,7522, 6781,3998,6619,6083,3903,3836,7353,6002,7495,7944,3579,6839,5622,6057,7754,7564,5975,5 867,7469,7374,7106,6044,7279,7011,7840,5949,5854,7512,4066,6631,5759,7080,5625,6998,78 13,6890,5111,7732,4039,7570,7053,3958,7475,7408,6972,6863,7761,6782,4013,6648,6112,738 1,7001,3823,7354,7524,7707,4056,6621,6085,6058,3961,7327,6004,7059,7470,3581,6897,6031, 7756,4019,5950,5869,7499,7108,6843,5626,7013,7814,5979,7719,4068,7585,7054,5599,7952,7 395,6959,6892,6065,7762,7572,4014,6635,5875,7477,7382,7002,7817,7287,5115,7736,4043,66 22,6086,3962,6527,7356,5991,7088,7709,3582,6898,6060,3935,7385,7061,5870,7528,6871,608 9,7014,4021,6008,7501,3831,7586,6845,5628,7939,7872,5981,3071,6066,7777,7559,7112,7478, 7397,7017,7818,6039,7764,7723,4072,6637,5877,7507,7004,7343,7075,5117,7710,4045,7576,5 823,3964,7481,7386,7062,7291,6967,6900,6090,4022,6643,5995,7502,7825,6846,5615,7968,40 51,5982,7065,7778,7588,6875,7941,7398,7018,4025,6068,7751,7617,3835,6638,5878,7536,699 1,7820,6097,5118,7725,4046,7563,7509,3951,7482,7401,7077,6043,7768,6887,5881,7455,7388, 7120,7293,7025,7826,6092,7731,4080,6645,5997,7066,7351,6971,6904,7942,4053,4026,6591,6 055,7780,7618,6877,7523,7020,3999,6098,7726,3837,7592,6003,7510,7945,7402,7078,5623,60 72,7755,7565,5882,7484,7375,7107,6045,7294,7026,7841,5855,7513,4067,6646,5998,7081,699 9,7828,6891,7733,4054,7571,7068,3959,7409,6973,6878,8000,6783,4028,6649,6113,7620,3838, 7355,7525,7946,4057,6100,6059,7784,7566,6005,7471,7404,7136,6046,7757,7842,5951,5884,7 514,7109,7082,5627,7028,7815,7734,4069,7600,7055,7953,7410,6974,6893,7763,7573,4015,66 50,6114,7383,7003,7832,7526,7737,4058,6623,6087,3963,7357,6006,7089,7948,3583,6899,606 1,7758,7624,5871,7529,7110,6104,7015,7844,6009,7516,4070,7587,7084,5629,7954,7873,6894, 6067,7792,7574,7113,7479,7412,7032,7819,7765,7738,4073,6652,6116,7005,7358,7090,7711,4 060,7577,6062,3965,7387,7063,7530,6901,6091,4023,6010,7503,8064,6847,5630,7969,7874,59 83,7779,7589,7114,7956,7399,7019,7848,6069,7766,7632,4074,6639,5879,7537,7006,7821,511 9,7740,4047,7578,3966,7483,7416,7092,7769,6902,6120,7389,7121,7532,7827,6093,7970,4081, 6012,7067,7590,6905,7943,7876,4027,6070,7781,7619,7116,7538,7021,7822,6099,7727,4076,7 593,7511,7960,7403,7079,6073,7770,7580,5883,7485,7390,7122,7295,7027,7856,6094,4082,66 47,5999,7096,7829,6906,7972,4055,7069,7782,7648,6879,8001,7022,4029,6128,7621,3839,759 4,7540,7947,7880,6101,6074,7785,7567,7486,7405,7137,6047,7772,7843,5885,7515,7124,7083, 7029,7830,7735,4084,7601,7070,7411,6975,6908,8002,4030,6651,6115,7622,7833,7527,7976,4 059,6102,7786,7596,6007,7949,7406,7138,6076,7759,7625,5886,7544,7111,6105,7030,7845,75 17,4071,7602,7085,7955,7888,6895,7793,7575,7128,7413,7033,7834,8004,7739,4088,6653,611 7,7359,7091,7950,4061,6063,7788,7626,7531,7140,6106,7846,6011,7518,8065,7086,5631,7984, 7875,7794,7604,7115,7957,7414,7034,7849,7767,7633,4075,6654,6118,7007,7836,7741,4062,7 579,3967,7417,7093,8008,6903,6121,7628,7533,8066,6108,7971,7904,6013,7591,7144,7958,78 77,7850,6071,7796,7634,7117,7539,7036,7823,7742,4077,7608,7961,7418,7094,7771,7581,612 2,7391,7123,7534,7857,6095,4083,6014,7097,8068,6907,7973,7878,7783,7649,7118,8016,7023, 7852,6129,7636,4078,7595,7541,7962,7881,6075,7800,7582,7487,7420,7152,7773,7858,6124,7 125,7098,7831,7974,4085,7071,7650,6909,8003,4031,6130,7623,8072,7542,7977,7882,6103,77 87,7597,7964,7407,7139,6077,7774,7640,5887,7545,7126,7031,7860,4086,7603,7100,7889,691 0,8032,7129,7652,7835,8005,7978,4089,6132,7598,7951,7884,6078,7789,7627,7546,7141,6107, 7847,7519,8080,7087,7985,7890,7795,7605,7130,7415,7035,7864,8006,4090,6655,6119,7837,7 980,4063,7790,7656,8009,7142,6136,7629,7548,8067,6109,7986,7905,7606,7145,7959,7892,78 51,7797,7635,7132,7037,7838,7743,4092,7609,7419,7095,8010,6123,7630,7535,8096,6110,790 6,6015,8069,7146,7988,7879,7798,7664,7119,8017,7038,7853,7637,4079,7610,7963,7896,7801, 7583,7421,7153,8012,7859,6125,7099,8070,7975,7908,7651,7148,8018,7854,6131,7638,8073,7 543,7992,7883,7802,7612,7965,7422,7154,7775,7641,6126,7127,7861,4087,7101,8128,6911,80 33,7653,8074,8020,7979,7912,6133,7599,7966,7885,6079,7804,7642,7547,7156,7862,8081,710 2,7891,8034,7131,7654,7865,8007,4091,6134,8076,7981,7886,7791,7657,8024,7143,6137,7644, 7549,8082,7987,7920,7607,7160,7893,7866,8036,7133,7839,7982,4093,7658,8011,6138,7631,7 550,8097,6111,7907,8084,7147,7989,7894,7799,7665,7134,7039,7868,4094,7611,7897,8040,76 60,8013,8098,6140,8071,7990,7909,7666,7149,8019,7855,7639,8088,7993,7898,7803,7613,742 3,7155,8014,6127,8100,7910,8129,7150,8048,7668,8075,8021,7994,7913,7614,7967,7900,7805, 7643,7157,7863,7103,8130,8035,7655,8104,8022,7914,6135,8077,7996,7887,7806,7672,8025,7 158,7645,8083,7921,7161,8132,7867,8037,8078,7983,7916,7659,8026,6139,7646,7551,8112,79 22,8085,7162,7895,8038,7135,7869,4095,8136,8041,7661,8028,8099,6141,8086,7991,7924,766 7,7164,7870,8089,7899,8042,7662,8015,6142,8101,7911,8144,7151,8049,7669,8090,7995,7928, 7615,7901,8044,8102,8131,8050,7670,8105,8023,7915,8092,7997,7902,7807,7673,7159,8160,8 133,8106,8052,8079,7998,7917,7674,8027,7647,8113,7923,7163,8134,8039,8108,7918,8137,80 56,7676,8029,8114,8087,7925,7165,7871,8138,8043,7663,8030,6143,8116,7926,8145,7166,809 1,7929,8140,8045,8103,8146,8051,7671,8120,7930,8093,7903,8046,8161,8148,8107,8053,8094, 7999,7932,7675,8162,8135,8054,8109,7919,8152,8057,7677,8115,8164,8110,8139,8058,7678,8 031,8117,7927,7167,8168,8141,8060,8118,8147,8121,7931,8142,8047,8176,8149,8122,8095,79 33,8163,8150,8055,8124,7934,8153,8165,8111,8154,8059,7679,8166,8169,8156,8061,8119,817 0,8143,8062,8177,8123,8172,8178,8151,8125,7935,8180,8126,8155,8167,8184,8157,8171,8158, 8063,8173,8179,8174,8181,8127,8182,8185,8186,8159,8188,8175,8183,8187,8189,8190,8191,],
• wherein when the mother code length is 4096, the first sequence is the sequence Q1, and wherein when the mother code length N is 4096, a quantity K of the K bits is 452, 536, 904, 1048, 1808, 2072, 2712, or 3096;
• and
• transmit the encoded bits over a wireless network.