Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum generalized Reed-Solomon codes: Unified framework for quantum
  MDS codes   We construct a new family of quantum MDS codes from classical generalized
Reed-Solomon codes and derive the necessary and sufficient condition under
which these quantum codes exist. We also give code bounds and show how to
construct them analytically. We find that existing quantum MDS codes can be
unified under these codes in the sense that when a quantum MDS code exists,
then a quantum code of this type with the same parameters also exists. Thus as
far as is known at present, they are the most important family of quantum MDS
codes.

15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
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
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas