On the ideal associated to a linear code

Abstract : 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 degree-compatible 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.
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Article dans une revue
Advances in Mathematics of Communications, AIMS, 2015
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https://hal.inria.fr/hal-01243389
Contributeur : Irene Márquez Corbella <>
Soumis le : mardi 15 décembre 2015 - 00:23:01
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

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  • HAL Id : hal-01243389, version 1
  • ARXIV : 1206.5124

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Irene Márquez-Corbella, Edgar Martinez-Moro, Suárez-Canedo Emilio. On the ideal associated to a linear code. Advances in Mathematics of Communications, AIMS, 2015. 〈hal-01243389〉

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