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

Manuel González Sarabia

doi:10.1515/auom-2016-0041

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 C_X(d) and C_X′(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 T_n₁-1 and T_n₂-1.

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

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