<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

Published Online: Sep 21, 2017

Page range: 261 - 270

Received: Apr 14, 2015

Accepted: Jun 30, 2015

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

Keywords
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

Published Online: Sep 21, 2017

Page range: 261 - 270

Received: Apr 14, 2015

Accepted: Jun 30, 2015

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

KeywordsToric set, Parameterized code, Relative generalized Hamming weight

© 2017

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

Keywords
Toric set, Parameterized code, Relative generalized Hamming weight