Parity check matrix creation method, encoding apparatus, and recording/reproduction apparatus

A parity check matrix creation method comprising:

• creating a mask matrix whose column weight is K (K is an integer not less than 2) by assigning one of “1” and “0” to each element of M rows×N columns (M is an integer not less than 4, and N is an integer larger than M);
• and
• creating a parity check matrix by, for each element in the mask matrix, arranging a cyclic permutation matrix having P rows×P columns (P is an integer not less than 2) at a corresponding position when the element is “1” and arranging a zero matrix having P rows×P columns at a corresponding position when the element is “0”,
• wherein all of N column vectors in the mask matrix are different from each other,
• a submatrix having M rows×L columns (L is an integer not more than (M−K+1−S) and S is an integer not less than 1) obtained by arbitrarily extracting L continuous columns from the mask matrix includes:
• B1 (B1 is an integer not less than 1) first correction rows;
• and
• Bi (Bi is an integer not less than 1, i is any integer not less than 2 and not more than I, and I is an integer not less than 2) ith correction rows,
• each of the B1 first correction rows has a row weight of 1,
• the B1 first correction rows have at least one “1” in total in each of A1 (A1 is an integer not less than 1) first correction columns,
• each of the Bi ith correction rows has a row weight of not less than 2,
• each of the Bi ith correction rows has at least one “1” in total in Ai−1 (Ai−1 is an integer not less than 1 and not more than Bi−1) (i−1)th correction columns,
• each of the B1 ith correction rows has “1” in one of Ai (Ai is an integer not less than 1 and not more than Bi) ith correction columns included in a column set excluding the first correction column to the (i−1)th correction column,
• the Bi ith correction rows include at least one “1” in total in each of the Ai ith correction columns,
• a sum from A1 to AI equals L,
• Bi is not more than Ai−1×(K−1), and
• a sum from B1 to BI−1 equals a sum of S and a sum from A1 to AI−1.