Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropic matroids and their representation   This paper investigates entropic matroids, that is, matroids whose rank
function is given as the Shannon entropy of random variables. In particular, we
consider $p$-entropic matroids, for which the random variables each have
support of cardinality $p$. We draw connections between such entropic matroids
and secret-sharing matroids and show that entropic matroids are linear matroids
when $p = 2,3$ but not when $p = 9$. Our results leave open the possibility for
$p$-entropic matroids to be linear whenever $p$ is prime, with particular cases
proved here. Applications of entropic matroids to coding theory and
cryptography are also discussed.

30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph