We study the relationship between a q-analogue of matroids and linear codes
with the rank metric in the vector space of matrices with entries in a finite
field. We prove a Greene type identity for the rank generating function of
these matroidal structures and the rank weight enumerator of these linear
codes. As an application, we give a combinatorial proof of a MacWilliams type
identity for Delsarte rank-metric codes.Comment: 16 page