A commutative algebra approach to linear codes

JOURNAL OF ALGEBRA

卷:321

Article

Giorgetti, Marta²  Sala, Massimiliano¹ 

[1] Univ Trento, Dept Math, Trento, Italy

[2] Univ Milan, Dept Math, I-20122 Milan, Italy

关键词: Linear code;    Distance;    Weight distribution;    Grobner basis;    General error locator polynomial;   

DOI  :  10.1016/j.jalgebra.2008.09.037

来源: Elsevier

【 摘 要 】

Recently some methods have been proposed to find the distance and weight distribution of cyclic codes using Grobner bases. We identify a class of codes for which these methods can be generalized. We show that this class contains all interesting linear codes and we provide variants and improvements. This approach sometimes reveals an unexpected algebraic structure in the code. We also investigate the decoding for a subclass, proving the existence of general error locator polynomials. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free