Sequence Determining Method and Apparatus

An apparatus, comprising:

• a storage medium including executable instructions;
• and
• at least one processor;
• wherein the executable instructions, when executed by the at least one processor, cause the apparatus to:
• determine an index v of a sequence group, wherein the sequence group comprises a sequence {xn} and a sequence {ym};
• and
• generate at least one of a second sequence {fn} or a second sequence {gm} based on the index v of the sequence group, wherein:
• the sequence {xn} corresponds to the second sequence {fn}, and the sequence {ym} corresponds to the second sequence {gm}, fn is an element in the second sequence {fn}, wherein gm is an element in the second sequence {gm}, a length of the second sequence {fn} is N, a length of the second sequence {gm} is M, n and m are integers, 0≤n≤N−1, and 0≤m≤M−1;
• the element fn satisfies fn=A·xnej·α·n;
• the element gm satisfies gm=A·ym·ej·α·m;
• A is a non-zero complex number, α is a real number, and j=√{square root over (−1)};
• an element xn in the sequence {xn} satisfies xn=u·eπ·j·sn/4, wherein u is a non-zero complex number, and sn is an element in a sequence {sn};
• an element ym in the sequence {ym} satisfies ym=kq(m mod Mprime),
• k
• q
• 
• (
• i
• )
• =
• e
• -
• j
• ·
• π
• ·
• q
• ·
• i
• ·
• (
• i
• +
• 1
• )
• M
• prime
• wherein, i is an integer, 0≤i≤Mprime−1, Mprime is a largest prime number that is smaller than M, q=┘q+1/2┘, and q=Mprime·(v+1)/31;
• and
• when N=24, a combination of the sequence {sn} and v is at least one of the following combination set:
• the sequence {sn} is {−1, −3, 3, −1, 3, 1, 3, −1, 1, −3, −1, −3, −1, 1, 3, −3, −1, −3, 3, 3, 3, −3, −3, −3}, and v=
• 0;
• the sequence {sn} is {−1, −3, 3, 1, 1, −3, 1, −3, −3, 1, −3, −1, −1, 3, −3, 3, 3, 3, −3, 1, 3, 3, −3, −3}, and
• v=1;
• the sequence {sn} is {1, −3, 3, −1, −3, −1, 3, 3, 1, −1, 1, 1, 3, −3, −1, −3, −3, −3, −1, 3, −3, −1, −3, −3}, and v=3;
• the sequence {sn} is {−1, 3, −3, −3, −1, 3, −1, −1, 1, 3, 1, 3, −1, −1, −3, 1, 3, 1, −1, −3, 1, −1, −3, −3}, and v=4;
• the sequence {sn} is {−3, −1, 1, −3, −3, 1, 1, −3, 3, −1, −1, −3, 1, 3, 1, −1, −3, −1, −3, 1, −3, −3, −3, −3}, and v=
• 5;
• the sequence {sn} is {−3, 1, 3, −1, 1, −1, 3, −3, 3, −1, −3, −1, −3, 3, −1, −1, −1, −3, −1, −1, −3, 3, 3, −3}, and v=7;
• the sequence {sn} is {−3, 1, −3, 3, −1, −1, −1, −3, 3, 1, −1, −3, −1, 1, 3, −1, 1, −1, 1, −3, −3, −3, −3, −3}, and v=
• 8;
• the sequence {sn} is {1, 1, −1, −3, −1, 1, 1, −3, 1, −1, 1, −3, 3, −3, −3, 3, −1, −3, 1, 3, −3, 1, −3, −3}, and v=9;
• the sequence {sn} is {−3, −3, −3, −1, 3, −3, 3, 1, 3, 1, −3, −1, −1, −3, 1, 1, 3, 1, −1, −3, 3, 1, 3, −3}, and v=10;
• the sequence {sn} is {−3, 3, −1, 3, 1, −1, −1, −1, 3, 3, 1, 1, 1, 3, 3, 1, −3, −3, −1, 1, −3, 1, 3, −3}, and v=11;
• the sequence {sn} is {3, −3, 3, −1, −3, 1, 3, 1, −1, −1, −3, −1, 3, −3, 3, −1, −1, 3, 3, −3, −3, 3, −3, −3}, and v=
• 12;
• the sequence {sn} is {−3, 3, −1, 3, −1, 3, 3, 1, 1, −3, 1, 3, −3, 3, −3, −3, −1, 1, 3, −3, −1, −1, −3, −3}, and v=13;
• the sequence {sn} is {−3, 1, −3, −1, −1, 3, 1, 3, −3, 1, −1, 3, 3, −1, −3, 3, −3, −1, −1, −3, −3, −3, 3, −3}, and v=
• 14;
• the sequence {sn} is {−3, −1, −1, −3, 1, −3, −3, −1, −1, 3, −1, 1, −1, 3, 1, −3, −1, 3, 1, 1, −1, −1, −3, −3}, and v=
• 15;
• the sequence {sn} is {3, −1, 3, −1, 1, −3, 1, 1, −3, −3, 3, −3, −1, −1, −1, −1, −1, −3, −3, −1, 1, 1, −3, −3}, and v=
• 17;
• the sequence {sn} is {−3, 1, −3, 1, −3, −3, 1, −3, 1, −3, −3, −3, −3, −3, 1, −3, −3, 1, 1, −3, 1, 1, −3, −3}, and v=
• 18;
• the sequence {sn} is {−3, −3, 3, 3, 1, −1, −1, −1, 1, −3, −1, 1, −1, 3, −3, −1, −3, −1, −1, 1, −3, 3, −1, −3}, and v=
• 19;
• the sequence {sn} is {−3, −3, −1, −1, −1, −3, 1, −1, −3, −1, 3, −3, 1, −3, 3, −3, 3, 3, 1, −1, −1, 1, −3, −3}, and v=
• 20;
• the sequence {sn} is {−3, 1, −3, 3, −3, 1, −3, 3, 1, −1, −3, −1, −3, −3, −3, −3, 1, 3, −1, 1, 3, 3, 3, −3}, and v=22;
• the sequence {sn} is {−3, −1, 1, −3, −1, −1, 1, 1, 1, 3, 3, −1, 1, −1, 1, −1, −1, −3, −3, −3, 3, 1, −1, −3}, and v=
• 23;
• the sequence {sn} is {−3, 3, −1, −3, −1, −1, −1, 3, −1, −1, 3, −3, −1, 3, −3, 3, −3, −1, 3, 1, 1, −1, −3, −3}, and v=
• 24;
• the sequence {sn} is {−3, 1, −1, −3, −3, −1, 1, −3, −1, −3, 1, 1, −1, 1, 3, 3, 3, −1, 1, −1, 1, −1, −3}, and v=
• 25;
• the sequence {sn} is {−1, 3, −1, −1, 3, 3, −1, −1, −1, 3, −1, −3, 1, 3, 1, 1, −3, −3, −3, −1, −3, −1, −3, −3}, and v=
• 26;
• the sequence {sn} is {−3, 1, −3, 1, −3, 1, 1, 3, 1, −3, −3, −1, 1, 3, −1, −3, 3, 1, −1, −3, −3, −3, −3, −3}, and v=
• 28;
• the sequence {sn} is {3, −3, −1, 1, 3, −1, −1, −3, −1, 3, −1, −3, −1, −3, 3, −1, 3, 1, 1, −3, 3, −3, −3, −3}, and v=
• 29.

A non-transitory computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the following:

• determining an index v of a sequence group, wherein the sequence group comprises a sequence {xn} and a sequence {ym};
• and
• generating at least one of a second sequence {fn} or a second sequence {gm} based on the index v of the sequence group, wherein:
• the sequence {xn} corresponds to the second sequence {fn}, and the sequence {ym} corresponds to the second sequence {gm}, fn is an element in the second sequence {fn}, wherein gm is an element in the second sequence {gm}, a length of the second sequence {fn} is N, a length of the second sequence {gm} is M, n and m are integers, 0≤n≤N−1, and 0≤m≤M−1;
• the element fn satisfies fn=A·xn·ej·α·n;
• the element gm satisfies gm=A·ym·ej·α·m;
• A is a non-zero complex number, a is a real number, and j=√{square root over (−1)};
• an element xn in the sequence {xn} satisfies xn=u·eπ·j·sn/4, wherein u is a non-zero complex number, and sn is an element in a sequence {sn};
• an element ym in the sequence {ym} satisfies ym=kq(m mod Mprime),
• k
• q
• 
• (
• i
• )
• =
• e
• -
• j
• ·
• π
• ·
• q
• ·
• i
• ·
• (
• i
• +
• 1
• )
• M
• prime
• wherein, i is an integer, 0≤i≤Mprime−1, Mprime is a largest prime number that i smaller than M, q=└q+1/2┘, and q=Mprime·(v+1)/31;
• and
• when N=24, a combination of the sequence {sn} and v is at least one of the following combination set:
• the sequence {sn} is {−1, −3, 3, −1, 3, 1, 3, −1, 1, −3, −1, −3, −1, 1, 3, −3, −1, −3, 3, 3, 3, −3, −3, −3}, and v=0;
• the sequence {sn} is {(−1, −3, 3, 1, 1, −3, 1, −3, −3, 1, −3, −1, −1, 3, −3, 3, 3, 3, −3, 1, 3, 3, −3, −3}, and v=1;
• the sequence {sn} is {1, −3, 3, −1, −3, −1, 3, 3, 1, −1, 1, 1, 3, −3, −1, −3, −3, −3, −1, 3, −3, −1, −3, −3}, and v=3;
• the sequence {sn} is {−1, 3, −3, −3, −1, 3, −1, −1, 1, 3, 1, 3, −1, −1, −3, 1, 3, 1, −1, −3, 1, −1, −3, −3}, and v=4;
• the sequence {sn} is {−3, −1, 1, −3, −3, 1, 1, −3, 3, −1, −1, −3, 1, 3, 1, −1, −3, −1, −3, 1, −3, −3, −3, −3}, and v=5;
• the sequence {sn} is {−3, 1, 3, −1, 1, −1, 3, −3, 3, −1, −3, −1, −3, 3, −1, −1, −1, −3, −1, −1, −3, 3, 3, −3}, and v=7;
• the sequence {sn} is {−3, 1, −3, 3, −1, −1, −1, −3, 3, 1, −1, −3, −1, 1, 3, −1, 1, −1, 1, −3, −3, −3, −3, −3}, and v=8;
• the sequence {sn} is {1, 1, −1, −3, −1, 1, 1, −3, 1, −1, 1, −3, 3, −3, −3, 3, −1, −3, 1, 3, −3, 1, −3, −3}, and v=9;
• the sequence {sn} is {−3, −3, −3, −1, 3, −3, 3, 1, 3, 1, −3, −1, −1, −3, 1, 1, 3, 1, −1, −3, 3, 1, 3, −3}, and v=10;
• the sequence {sn} is {−3, 3, −1, 3, 1, −1, −1, −1, 3, 3, 1, 1, 1, 3, 3, 1, −3, −3, −1, 1, −3, 1, 3, −3}, and v=11;
• the sequence {sn} is {3, −3, 3, −1, −3, 1, 3, 1, −1, −1, −3, −1, 3, −3, 3, −1, −1, 3, 3, −3, −3, 3, −3, −3}, and v=12;
• the sequence {sn} is {−3, 3, −1, 3, −1, 3, 3, 1, 1, −3, 1, 3, −3, 3, −3, −3, −1, 1, 3, −3, −1, −1, −3, −3}, and v=13;
• the sequence {sn} is {−3, 1, −3, −1, −1, 3, 1, 3, −3, 1, −1, 3, 3, −1, −3, 3, −3, −1, −1, −3, −3, −3, 3, −3}, and v=14;
• the sequence {sn} is {−3, −1, −1, −3, 1, −3, −3, −1, −1, 3, −1, 1, −1, 3, 1, −3, −1, 3, 1, 1, −1, −1, −3, −3}, and v=15;
• the sequence {sn} is {3, −1, 3, −1, 1, −3, 1, 1, −3, −3, 3, −3, −1, −1, −1, −1, −1, −3, −3, −1, 1, 1, −3, −3}, and v=17;
• the sequence {sn} is {−3, 1, −3, 1, −3, −3, 1, −3, 1, −3, −3, −3, −3, −3, 1, −3, −3, 1, 1, −3, 1, 1, −3, −3}, and v=18;
• the sequence {sn} is {−3, −3, 3, 3, 1, −1, −1, −1, 1, −3, −1, 1, −1, 3, −3, −1, −3, −1, −1, 1, −3, 3, −1, −3}, and v=19;
• the sequence {sn} is {−3, −3, −1, −1, −1, −3, 1, −1, −3, −1, 3, −3, 1, −3, 3, −3, 3, 3, 1, −1, −1, 1, −3, −3}, and v=20;
• the sequence {sn} is {−3, 1, −3, 3, −3, 1, −3, 3, 1, −1, −3, −1, −3, −3, −3, −3, 1, 3, −1, 1, 3, 3, 3, −3}, and v=22;
• the sequence {sn} is {−3, −1, 1, −3, −1, −1, 1, 1, 1, 3, 3, −1, 1, −1, 1, −1, −1, −3, −3, −3, 3, 1, −1, −3}, and v=23;
• the sequence {sn} is {−3, 3, −1, −3, −1, −1, −1, 3, −1, −1, 3, −3, −1, 3, −3, 3, −3, −1, 3, 1, 1, −1, −3, −3}, and v=24;
• the sequence {sn} is {−3, 1, −1, −3, −3, −1, 1, −3, −1, −3, 1, 1, −1, 1, 1, 3, 3, −1, 1, −1, 1, −1, −3}, and v=25;
• the sequence {sn} is {−1, 3, −1, −1, 3, 3, −1, −1, −1, 3, −1, −3, 1, 3, 1, 1, −3, −3, −3, −1, −3, −1, −3, −3}, and v=26;
• the sequence {sn} is {−3, 1, −3, 1, −3, 1, 1, 3, 1, −3, −3, −1, 1, 3, −1, −3, 3, 1, −1, −3, −3, −3, −3, −3}, and v=28;
• the sequence {sn} is {3, −3, −1, 1, 3, −1, −1, −3, −1, 3, −1, −3, −1, −3, 3, −1, 3, 1, 1, −3, 3, −3, −3, −3}, and v=29.