A symmetric Roos bound for linear codes

Abstract

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 q 2 − 1 over F q . We give cyclic codes [ 63 , 38 , 16 ] and [ 65 , 40 , 16 ] over F 8 that are better than the known [ 63 , 38 , 15 ] and [ 65 , 40 , 15 ] codes.