<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we find some bounds for the relative generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. Also we compare the relative generalized Hamming weights of the codes CX(d) and CX′(d) when X′ is embedded in X. We use these results to obtain some lower bounds for the relative generalized Hamming weights of the codes parameterized by the edges of any connected bipartite graph with bipartition (V1, V2) and where |V1| = n1, |V2| = n2, in terms of the relative generalized Hamming weights of the codes associated to the projective tori Tn₁-1 and Tn₂-1. </abstract>

In this paper we find some bounds for the relative generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. Also we compare the relative generalized Hamming weights of the codes CX(d) and CX′(d) when X′ is embedded in X. We use these results to obtain some lower bounds for the relative generalized Hamming weights of the codes parameterized by the edges of any connected bipartite graph with bipartition (V1, V2) and where |V1| = n1, |V2| = n2, in terms of the relative generalized Hamming weights of the codes associated to the projective tori Tn₁-1 and Tn₂-1.

Some bounds for the relative generalized Hamming weights of some evaluation codes

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper we find some bounds for the relative generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. Also we...

Some bounds for the relative generalized Hamming weights of some evaluation codes

Publié en ligne: 21 sept. 2017

Pages: 261 - 270

Reçu: 14 avr. 2015

Accepté: 30 juin 2015

DOI: https://doi.org/10.1515/auom-2016-0041

Mots clés
Toric set, Parameterized code, Relative generalized Hamming weight

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Some bounds for the relative generalized Hamming weights of some evaluation codes

Publié en ligne: 21 sept. 2017

Pages: 261 - 270

Reçu: 14 avr. 2015

Accepté: 30 juin 2015

DOI: https://doi.org/10.1515/auom-2016-0041

Mots clésToric set, Parameterized code, Relative generalized Hamming weight

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
Toric set, Parameterized code, Relative generalized Hamming weight