A BCH Code and a Sequence of Cyclic Codes

This study establishes that for a given binary BCH code C 0 n of length n generated by a polynomial g(x) ∈ F2[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