March 30, 2018 / / in cs updates on arXiv.org / with No comments /
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.
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