Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple Quantum Error Correcting Codes   Methods of finding good quantum error correcting codes are discussed, and
many example codes are presented. The recipe C_2^{\perp} \subseteq C_1, where
C_1 and C_2 are classical codes, is used to obtain codes for up to 16
information qubits with correction of small numbers of errors. The results are
tabulated. More efficient codes are obtained by allowing C_1 to have reduced
distance, and introducing sign changes among the code words in a systematic
manner. This systematic approach leads to single-error correcting codes for 3,
4 and 5 information qubits with block lengths of 8, 10 and 11 qubits
respectively.

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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci