A BCH code and a sequence of cyclic codes

Abstract

This study establishes that for a given binary BCH code C 0 n of length n generated by a polynomial g(x) ∈ F 2 [x] of degree r there exists a family of binary cyclic codes {C m 2 m−1 (n+1)n } m≥1 such that for each m ≥ 1, the binary cyclic code C m 2 m−1 (n+1)n has length 2 m−1 (n + 1)n and is generated by a generalized polynomial g(x2 m (n+1)n for each m ≥ 1. By a newly proposed algorithm, codewords of the binary BCH code C 0 n can be transmitted with high code rate and decoded by the decoder of any member of the family {C m 2 m−1 (n+1)n } m≥1 of binary cyclic codes, having the same code rate.Mathematics Subject Classification: 11T71, 14A50, 94A15