A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code

Abstract

For a given binary BCH code Cn of length n = 2s-1 generated by a polynomial g(x)e{open}F2[x] of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial g(x1/2)e{open}F2[x1/2ℤ ≥ 0] of degree 2r. However, it does exist a binary cyclic code C(n+1)n of length (n + 1)n such that the binary BCH code Cn is embedded in C(n+1)n. Accordingly a high code rate is attained through a binary cyclic code C(n+1)n for a binary BCH code Cn. Furthermore, an algorithm proposed facilitates in a decoding of a binary BCH code Cn through the decoding of a binary cyclic code C(n+1)n, while the codes Cn and C(n+1)n have the same minimum hamming distance.