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arXiv · 1904.01913

A Polymatroid Approach to Generalized Weights of Rank Metric Codes

Sudhir R. Ghorpade·Trygve Johnsen
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Abstract

We consider the notion of a $(q,m)$-polymatroid, due to Shiromoto, and the more general notion of $(q,m)$-demi-polymatroid, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality for generalized Hamming weights of linear codes. The corresponding results of Ravagnani for Delsarte rank metric codes, and Martinez-Penas and Matsumoto for relative generalized rank weights are derived as a consequence.

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Sudhir R. Ghorpade, Trygve Johnsen. 2019-04-03. A Polymatroid Approach to Generalized Weights of Rank Metric Codes. https://arxiv.org/abs/1904.01913

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