Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weight and rank of matrices over finite fields   Define the weight of a matrix to be the number of non-zero entries. One would
like to count $m$ by $n$ matrices over a finite field by their weight and rank.
This is equivalent to determining the probability distribution of the weight
while conditioning on the rank. The complete answer to this question is far
from finished. As a step in that direction this paper finds a closed form for
the average weight of an $m$ by $n$ matrix of rank $k$ over the finite field
with $q$ elements. The formula is a simple algebraic expression in $m$, $n$,
$k$, and $q$. For rank one matrices a complete description of the weight
distribution is given and a central limit theorem is proved.

14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys