A BCH Code and a Sequence of Cyclic Codes

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This study establishes that for a given binary BCH code C0n of length n generated by a polynomial g(x) ∈ F2[x] of degree r there exists a family of binary cyclic codes {Cm2m−1(n+1)n}m≥1 such that for each m ≥ 1, the binary cyclic code Cm2m−1(n+1)n has length 2 m−1(n + 1)n and is generated by a generalized polynomial g(x