Rank-metric codes and q-polymatroids

被引：0

作者：

Elisa Gorla

Relinde Jurrius

Hiram H. López

Alberto Ravagnani

机构：

[1] Université de Neuchâtel,Institut de Matématiques

[2] Netherlands Defence Academy,Faculty of Military Science

[3] Cleveland State University,Department of Mathematics

[4] University College Dublin,School of Mathematics and Statistics

来源：

Journal of Algebraic Combinatorics | 2020年 / 52卷

关键词：

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

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：1 / 19

页数：18

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