Betti Numbers and Generalized Hamming Weights - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2016

Betti Numbers and Generalized Hamming Weights

Abstract

We can associate to each linear code C defined over a finite field the matroid M[H] of its parity check matrix H. For any matroid M one can define its generalized Hamming weights which are the same as those of the code C. In [2] the authors show that the generalized Hamming weights of a matroid are determined by the N-graded Betti numbers of the Stanley-Reisner ring of the simplicial complex whose faces are the independent set of M. In this talk we go a step further. Our practical results indicate that the generalized Hamming weights of a linear code C can be obtained from the monomial ideal associated with a test-set for C. Moreover, recall that in [3] we use the Gröbner representation of a linear code C to provide a test-set for C. Our results are still a work in progress, but its applications to Coding Theory and Cryptography are of great value.
Fichier principal
Vignette du fichier
CACTC16-6.pdf (121.1 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01409298 , version 1 (05-12-2016)

Identifiers

  • HAL Id : hal-01409298 , version 1

Cite

Irene Márquez-Corbella, Edgar Martínez-Moro. Betti Numbers and Generalized Hamming Weights. 22nd Conference on Applications of Computer Algebra (ACA 2016), Aug 2016, Kassel, Germany. ⟨hal-01409298⟩

Collections

INRIA INRIA2
95 View
155 Download

Share

Gmail Mastodon Facebook X LinkedIn More