Skip to Main content Skip to Navigation
Journal articles

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.
Complete list of metadatas

https://hal.inria.fr/hal-01243389
Contributor : Irene Márquez Corbella <>
Submitted on : Tuesday, December 15, 2015 - 12:23:01 AM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM

Links full text

Identifiers

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

Collections

Citation

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⟩

Share

Metrics

Record views

192