Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: q-Polymatroids and Their Relation to Rank-Metric Codes   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.

0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph