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Título
On the ideal associated to a linear code
Año del Documento
2016
Editorial
American Institute of Mathematical Sciences
Descripción
Producción Científica
Documento Fuente
Advances in Mathematics of Communications, 2016, vol. 10, n. 2. p. 229-254
Resumo
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 binomials
involved 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 this
allows the description of a Hamming metric decoding procedure. Moreover,
the binomials involved in the Graver basis of I+(C) provide a universal test-set
which turns out to be a set containing the set of codewords of minimal support
of the code.
Palabras Clave
Gröbner bases
Bases de Gröbner
Graver bases
Bases de Graver
Linear codes
Códigos lineales
ISSN
1930-5338
Revisión por pares
SI
Patrocinador
Ministerio de Ciencia, Innovación y Universidades (projects MTM2007- 64704 / MTM2010-21580-C02-02)
Version del Editor
Propietario de los Derechos
© 2016 American Institute of Mathematical Sciences
Idioma
eng
Tipo de versión
info:eu-repo/semantics/publishedVersion
Derechos
openAccess
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