Skip to Main content Skip to Navigation
New interface
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 metadata
Contributor : Irene Márquez Corbella Connect in order to contact the contributor
Submitted on : Tuesday, December 15, 2015 - 12:23:01 AM
Last modification on : Friday, January 21, 2022 - 3:15:08 AM

Links full text


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



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



Record views