A polymatroid approach to generalized weights of rank metric codes

Abstract

We consider the notion of a (<i>q,m)</i>-polymatroid, due to Shiromoto, and the more general notion of (<i>q,m</i>)-demi-polymatroids, 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 Martínez-Peñas and Matsumoto for relative generalized rank weights are derived as a consequence.