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

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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.

Original languageEnglish
Pages (from-to)261-270
Number of pages10
JournalAnalele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
Volume24
Issue number2
DOIs
StatePublished - 2016

Keywords

  • Parameterized code
  • Relative generalized Hamming weight
  • Toric set

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