Rank-metric codes and q-polymatroids

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 invarian...

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Bibliographic Details
Published inJournal of algebraic combinatorics Vol. 52; no. 1; pp. 1 - 19
Main Authors Gorla, Elisa, Jurrius, Relinde, López, Hiram H., Ravagnani, Alberto
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2020
Springer Nature B.V
Subjects
Combinatorial analysis
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Generalized weights
MRD code
Duality
Rank-metric code
polymatroid
Optimal anticode
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Summary: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.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-019-00889-4