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

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Abstract

© 2016, Ovidius University. All rights reserved. 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 Tn1−1and Tn2−1.
Original languageAmerican English
Pages (from-to)261-270
Number of pages10
JournalAnalele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
DOIs
StatePublished - 1 Jan 2016

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Hamming Weight
Evaluation
Bipartite Graph
Connected graph
Torus
Lower bound

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title = "Some bounds for the relative generalized Hamming weights of some evaluation codes",
abstract = "{\circledC} 2016, Ovidius University. All rights reserved. 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 Tn1−1and Tn2−1.",
author = "{Gonz{\'a}lez Sarabia}, Manuel",
year = "2016",
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doi = "10.1515/auom-2016-0041",
language = "American English",
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journal = "Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica",
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publisher = "Ovidius University",

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N2 - © 2016, Ovidius University. All rights reserved. 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 Tn1−1and Tn2−1.

AB - © 2016, Ovidius University. All rights reserved. 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 Tn1−1and Tn2−1.

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