Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On sets of vectors of a finite vector space in which every subset of
  basis size is a basis II   This article contains a proof of the MDS conjecture for $k \leq 2p-2$. That
is, that if $S$ is a set of vectors of ${\mathbb F}_q^k$ in which every subset
of $S$ of size $k$ is a basis, where $q=p^h$, $p$ is prime and $q$ is not and
$k \leq 2p-2$, then $|S| \leq q+1$. It also contains a short proof of the same
fact for $k\leq p$, for all $q$.

28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin