Rank-Metric Codes and -Polymatroids
arXiv:1803.10844 · doi:10.1007/s10801-019-00889-4
Abstract
This paper contributes to the study of rank-metric codes from an algebraic and combinatorial point of view. We introduce -polymatroids, the -analogue of polymatroids, and develop their basic properties. We associate a pair of q-polymatroids to a rank-metric codes and show that several invariants and structural properties of the code, such as generalized weights, the property of being MRD or an optimal anticode, and duality, are captured by the associated combinatorial object.
Previous version has a typo in M_2 in Example 2.5