Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Binary additive MRD codes with minimum distance n-1 must contain a
  semifield spread set   In this paper we prove a result on the structure of the elements of an
additive {\it maximum rank distance (MRD) code} over the field of order two,
namely that in some cases such codes must contain a semifield spread set. We
use this result to classify additive MRD codes in $M_n(\mathbb{F}_2)$ with
minimum distance $n-1$ for $n\leq 6$. Furthermore we present a computational
classification of additive MRD codes in $M_4(\mathbb{F}_3)$. The computational
evidence indicates that MRD codes of minimum distance $n-1$ are much more rare
than MRD codes of minimum distance $n$, i.e. semifield spread sets. In all
considered cases, each equivalence class has a known algebraic construction.

16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg