A Polymatroid Approach to Generalized Weights of Rank Metric Codes

April 03, 2019 · Declared Dead · 🏛 Designs, Codes and Cryptography

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Authors Sudhir R. Ghorpade, Trygve Johnsen arXiv ID 1904.01913 Category cs.IT: Information Theory Cross-listed math.CO Citations 27 Venue Designs, Codes and Cryptography Last Checked 3 months ago
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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