q-Polymatroids associated with restricted rank-metric codes

Abstract

In this article, we study polymatroids that are representable by means of linear restricted rank-metric codes, namely, by subspaces of the space of alternating, symmetric, or Hermitian square matrices endowed with the rank metric. More precisely, we characterize the rank function defining these polymatroids and establish sufficient conditions on the relevant parameters under which it is fully determined. We show that there are several differences in compared to the behaviour of $q$-polymatroids of unrestricted matrix codes.