  It is well known that linear rank-metric codes give rise to q-polymatroids.
Analogously to matroid theory one may ask whether a given q-polymatroid is
representable by a rank-metric code. We provide an answer by presenting an
example of a q-matroid that is not representable by any linear rank-metric code
and, via a relation to paving matroids, provide examples of various q-matroids
that are not representable by F_{q^m}-linear rank-metric codes. We then go on
and introduce deletion and contraction for q-polymatroids and show that they
are mutually dual and correspond to puncturing and shortening of rank-metric
codes. Finally, we introduce a closure operator along with the notion of flats
and show that the generalized rank weights of a rank-metric code are fully
determined by the flats of the associated q-polymatroid.
