Rank-metric codes and q-polymatroids

Elisa Gorla (Corresponding author), Relinde Jurrius, Hiram H. López, Alberto Ravagnani

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

This paper contributes to the study of rank-metric codes from an algebraic and combinatorial point of view. We introduce q-polymatroids, the q-analogue of polymatroids, and develop their basic properties. We associate a pair of q-polymatroids with a rank-metric code and show that several invariants and structural properties of the code, such as generalized weights, the property of being MRD or an optimal anticode, and duality, are captured by the associated combinatorial object.

Original languageEnglish
Pages (from-to)1-19
JournalJournal of Algebraic Combinatorics
Volume52
Issue number1
DOIs
Publication statusPublished - 1 Aug 2020
Externally publishedYes

Keywords

  • Duality
  • Generalized weights
  • MRD code
  • Optimal anticode
  • q-polymatroid
  • Rank-metric code

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