On the ideal associated to a linear code

Irene Márquez-Corbella, Edgar Martínez-Moro, Emilio Suárez-Canedo

    Research output: Contribution to journalArticleResearchpeer-review

    2 Citations (Scopus)

    Abstract

    © 2016 AIMS. 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 Gröbner 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.
    Original languageEnglish
    Pages (from-to)229-254
    JournalAdvances in Mathematics of Communications
    Volume10
    Issue number2
    DOIs
    Publication statusPublished - 1 May 2016

    Keywords

    • Graver bases
    • Gröbner bases
    • Minimal support codewords

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