Parity check matrix, method of generating parity check matrix, encoding method and error correction apparatus

摘要

A parity check matrix making it possible to encode through decoding, a method of generating a parity check matrix, an encoding method and an error correction apparatus including defining an MxN parity check matrix H=[H_m|H_p], and generating an MxM matrix as a sub-matrix H_p wherein all row vectors are linearly independent, a set A of all of the row vectors is a union set of non-empty subsets A₁, A₂, . . . , A_k (1<=k<=M) that do not include intersection sets with each other, A₁ is a set of weight one row vectors, and A_i (2<=i<=k) is a set of row vectors capable of deriving a weight one row vector by a linear combination with row vectors in a union set of the subsets A₁, . . . , A_i-1 among the row vectors not included in the union set.