Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constrained Linear Representability of Polymatroids and Algorithms for
  Computing Achievability Proofs in Network Coding   The constrained linear representability problem (CLRP) for polymatroids
determines whether there exists a polymatroid that is linear over a specified
field while satisfying a collection of constraints on the rank function. Using
a computer to test whether a certain rate vector is achievable with vector
linear network codes for a multi-source network coding instance and whether
there exists a multi-linear secret sharing scheme achieving a specified
information ratio for a given secret sharing instance are shown to be special
cases of CLRP. Methods for solving CLRP built from group theoretic techniques
for combinatorial generation are developed and described. These techniques form
the core of an information theoretic achievability prover, an implementation
accompanies the article, and several computational experiments with interesting
instances of network coding and secret sharing demonstrating the utility of the
method are provided.

18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc