Rank-metric codes and q-polymatroids

Elisa Gorla; Relinde Jurrius; Hiram H. López; Alberto Ravagnani

doi:10.1007/s10801-019-00889-4

Rank-metric codes and q-polymatroids

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

Research output: Contribution to journal › Article › Academic › peer-review

13 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 language	English
Pages (from-to)	1-19
Number of pages	19
Journal	Journal of Algebraic Combinatorics
Volume	52
Issue number	1
DOIs	https://doi.org/10.1007/s10801-019-00889-4
Publication status	Published - 1 Aug 2020
Externally published	Yes

Keywords

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

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10.1007/s10801-019-00889-4

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KW - Generalized weights

KW - MRD code

KW - Optimal anticode

KW - q-polymatroid

KW - Rank-metric code

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Rank-metric codes and q-polymatroids

Abstract

Keywords

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