Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming
  Bound   I develop methods for analyzing quantum error-correcting codes, and use these
methods to construct an infinite class of codes saturating the quantum Hamming
bound. These codes encode $k=n-j-2$ qubits in $n=2^j$ qubits and correct $t=1$
error.

1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph