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

Manuel González Sarabia, Eduardo Camps, Eliseo Sarmiento, Rafael H. Villarreal

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper we give a formula for the second generalized Hamming weight of certain evaluation codes arising from a projective torus. This allows us to compute the corresponding weights of the codes parameterized by the edges of a complete bipartite graph. We determine some of the generalized Hamming weights of non-degenerate evaluation codes arising from a complete intersection in terms of the minimum distance, the degree and the a-invariant. It is shown that the generalized Hamming weights and the minimum distance have some similar behavior for parameterized codes These results are used to find the complete weight hierarchy of some codes.

Original languageEnglish
Pages (from-to)370-394
Number of pages25
JournalFinite Fields and their Applications
Volume52
DOIs
StatePublished - Jul 2018

Fingerprint

Hamming Weight
Torus
Evaluation
Minimum Distance
Weight Hierarchy
Complete Bipartite Graph
Complete Intersection
Invariant

Keywords

  • Complete intersection
  • Evaluation code
  • Generalized Hamming weight
  • Parameterized code

Cite this

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The second generalized Hamming weight of some evaluation codes arising from a projective torus. / González Sarabia, Manuel; Camps, Eduardo; Sarmiento, Eliseo; Villarreal, Rafael H.

In: Finite Fields and their Applications, Vol. 52, 07.2018, p. 370-394.

Research output: Contribution to journalArticle

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