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TitleA commutative algebra approach to linear codes
Author(s) Marta Giorgetti, Massimiliano Sala
TypeArticle in Journal
AbstractRecently some methods have been proposed to find the distance and weight distribution of cyclic codes using Gröbner 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.
KeywordsLinear code, Distance, Weight distribution, Gröbner basis, General error locator polynomial
ISSN0021-8693
URL http://www.sciencedirect.com/science/article/pii/S0021869308004997
LanguageEnglish
JournalJournal of Algebra
Volume321
Number8
Pages2259 - 2286
Year2009
NoteComputational Algebra
Edition0
Translation No
Refereed No
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