Rank-metric codes and q-polymatroids

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

Research output: Contribution to journalArticleAcademicpeer-review

25 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
Number of pages19
JournalJournal of Algebraic Combinatorics
Volume52
Issue number1
DOIs
Publication statusPublished - 1 Aug 2020
Externally publishedYes

Funding

Elisa Gorla was partially supported by the Swiss National Science Foundation through Grant No. 200021_150207. Hiram H. López was partially supported by SNI, Mexico. Alberto Ravagnani was partially supported by the Swiss National Science Foundation through Grant No. P2NEP2_168527.

FundersFunder number
Horizon 2020 Framework Programme740880
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung200021_150207
Sistema Nacional de InvestigadoresP2NEP2_168527

    Keywords

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

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