Rank-Metric Codes and q-Polymatroids

03/28/2018

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by   Elisa Gorla, et al.

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We study some algebraic and combinatorial invariants of rank-metric codes, specifically generalized weights. We introduce q-polymatroids, the q-analogue of polymatroids, and develop their basic properties. We show that rank-metric codes give rise to q-polymatroids, and that several of their structural properties are captured by the associated combinatorial object.