About the nth-root codes: A Gröbner basis approach to the weight computation

Abstract

Recently some methods have been proposed to find the distance and weight distribution of cyclic codes using Gröbner bases (Sala in Appl. Algebra Engrg. Comm. Comput. 13(2):137-162, 2002; Mora and Sala in J. Symbolic Comput. 35(2):177-194, 2003). We identify a class of codes for which these methods can be generalized. We show that this class contains all interesting linear codes (i.e., with d≥2) and we provide variants and improvements. © 2009 Springer-Verlag Berlin Heidelberg.