Elisa Gorla – University of Neuchâtel

Rank-metric codes and q-polymatroids

Rank-metric codes are vector subspaces of the vector space of matrices of given size over a finite field, equipped with the distance function induced by the rank. After an introduction to rank-metric codes, I will introduce q-polymatroids — the q-analogue of polymatroids — and associate a pair of q-polymatroids to each rank-metric codes. I will then discuss how several invariants and structural properties of a code, including generalized weights and duality, are captured by the associated q-polymatroids.