A symmetric Roos bound for linear codes

The van Lint–Wilson AB-method yields a short proof of the Roos bound for the minimum distance of a cyclic code. We use the AB-method to obtain a different bound for the weights of a linear code. In contrast to the Roos bound, the role of the codes A and B in our bound is symmetric. We use the bound to prove the actual minimum distance for a class of dual BCH codes of length q2−1 over Fq. We give cyclic codes [63,38,16] and [65,40,16] over F8 that are better than the known [63,38,15] and [65,40,15] codes.