A Polymatroid Approach to Generalized Weights of Rank Metric Codes

04/03/2019

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by   Sudhir R. Ghorpade, et al.

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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.