Classification of q-Ary Perfect Quantum Codes

We solve the problem of the classification of q -ary perfect quantum codes. We prove that the only nontrivial q -ary perfect quantum codes are those with the parameters ((( q 2 l - 1)/( q 2 - 1), qn - 2 l ,3)) q . There exist no other nontrivial q -ary perfect quantum codes.

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Bibliographic Details
Published in:IEEE transactions on information theory 2013-01, Vol.59 (1), p.631-634
Main Authors: Li, Zhuo, Xing, Lijuan
Format: Article
Language:English
Subjects:
Applied sciences
Classical and quantum physics: mechanics and fields
Classification
Codes
Coding theory
Coding, codes
Educational institutions
Error correction
Error correction codes
Exact sciences and technology
Indexes
Information theory
Information, signal and communications theory
Perfect quantum codes
Physics
Polynomials
quantum error-correcting codes
Quantum information
Quantum mechanics
Quantum theory
Signal and communications theory
Telecommunications and information theory
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Summary:We solve the problem of the classification of q -ary perfect quantum codes. We prove that the only nontrivial q -ary perfect quantum codes are those with the parameters ((( q 2 l - 1)/( q 2 - 1), qn - 2 l ,3)) q . There exist no other nontrivial q -ary perfect quantum codes.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2012.2217475