The second generalized Hamming weight of some evaluation codes arising from a projective torus

Finite Fields Appl. 52 (2018), 370--394 In this paper we find the second generalized Hamming weight of some evaluation codes arising from a projective torus, and it allows to compute the second generalized Hamming weight of the codes parameterized by the edges of any complete bipartite graph. Also,...

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Bibliographic Details
Main Authors Sarabia, Manuel González, Camps, Eduardo, Sarmiento, Eliseo, Villarreal, Rafael H
Format Journal Article
LanguageEnglish
Published 19.11.2016
Subjects
Computer Science - Information Theory
Mathematics - Algebraic Geometry
Mathematics - Commutative Algebra
Mathematics - Information Theory
Mathematics - Number Theory
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Summary:Finite Fields Appl. 52 (2018), 370--394 In this paper we find the second generalized Hamming weight of some evaluation codes arising from a projective torus, and it allows to compute the second generalized Hamming weight of the codes parameterized by the edges of any complete bipartite graph. Also, at the beginning, we obtain some results about the generalized Hamming weights of some evaluation codes arising from a complete intersection when the minimum distance is known and they are non--degenerate codes. Finally we give an example where we use these results to determine the complete weight hierarchy of some codes.
DOI:10.48550/arxiv.1611.06405