RT info:eu-repo/semantics/article
T1 On the ideal associated to a linear code
A1 Márquez Corbella, Irene
A1 Martínez Moro, Edgar
A1 Suárez Canedo, Emilio
K1 Gröbner bases
K1 Bases de Gröbner
K1 Graver bases
K1 Bases de Graver
K1 Linear codes
K1 Códigos lineales
AB This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal I+(C) to an arbitrary linear code. The binomialsinvolved in the reduced Gr¨obner basis of such an ideal relative to a degreecompatible ordering induce a uniquely defined test-set for the code, and thisallows the description of a Hamming metric decoding procedure. Moreover,the binomials involved in the Graver basis of I+(C) provide a universal test-setwhich turns out to be a set containing the set of codewords of minimal supportof the code.
PB American Institute of Mathematical Sciences
SN 1930-5338
YR 2016
FD 2016
LK http://uvadoc.uva.es/handle/10324/40725
UL http://uvadoc.uva.es/handle/10324/40725
LA eng
NO Advances in Mathematics of Communications, 2016, vol. 10, n. 2. p. 229-254
NO Producción Científica
DS UVaDOC
RD 22-nov-2024