arXiv subjects

Emilio Suárez-Canedo

Publications and source records attributed to Emilio Suárez-Canedo.

2 recordsLinked to original sources

arXiv2015

On the ideal associated to a linear code

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 $I_+(\mathcal C)$ to an arbitrary linear code. The binomials involved in the reduced Gröbner 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 $I_+(\mathcal C)$ provide a universal test-set which turns out to be a set containing the set of codewords of minimal support of the code.

cs.IT↗

arXiv2012

On the Composition of Secret Sharing Schemes Related to Codes

In this paper we construct a subclass of the composite access structure introduced by Martínez et al. based on schemes realizing the structure given by the set of codewords of minimal support of linear codes. This class enlarges the iterated threshold class studied in the same paper. Furthermore all the schemes on this paper are ideal (in fact they allow a vector space construction) and we arrived to give a partial answer to a conjecture stated in the above paper. Finally, as a corollary we proof that all the monotone access structures based on all the minimal supports of a code can be realized by a vector space construction.

cs.IT↗