Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum MDS Codes over Small Fields   We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$
with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how
starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic
codes, new QMDS codes can be obtained by shortening. We provide numerical
evidence for our conjecture that almost all admissible lengths, from a lower
bound $n_0(q,d)$ on, are achievable by shortening. Some additional codes that
fill gaps in the list of achievable lengths are presented as well along with a
construction of a family of QMDS codes of length $q^2+2$, where $q=2^m$, that
appears to be new.

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The categories of this paper are: eess
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin