Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Existence of Universally Decodable Matrices   Universally decodable matrices (UDMs) can be used for coding purposes when
transmitting over slow fading channels. These matrices are parameterized by
positive integers $L$ and $N$ and a prime power $q$. The main result of this
paper is that the simple condition $L \leq q+1$ is both necessary and
sufficient for $(L,N,q)$-UDMs to exist. The existence proof is constructive and
yields a coding scheme that is equivalent to a class of codes that was proposed
by Rosenbloom and Tsfasman. Our work resolves an open problem posed recently in
the literature.

14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph