Self-orthogonal codes with dual distance three and quantum codes with distance three over $$\mathbb F _5$$ F 5

Self-orthogonal codes with dual distance three and quantum codes with distance three over... Self-orthogonal codes with dual distance three and quantum codes with distance three constructed from self-orthogonal codes over $$\mathbb F _5$$ F 5 are discussed in this paper. Firstly, for given code length $$n\ge 5$$ n ≥ 5 , a $$[n,k]_{5}$$ [ n , k ] 5 self-orthogonal code with minimal dimension $$k$$ k and dual distance three is constructed. Secondly, for each $$n\ge 5$$ n ≥ 5 , two nested self-orthogonal codes with dual distance two and three are constructed, and consequently quantum code of length $$n$$ n and distance three is constructed via Steane construction. All of these quantum codes constructed via Steane construction are optimal or near optimal according to the quantum Hamming bound. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Self-orthogonal codes with dual distance three and quantum codes with distance three over $$\mathbb F _5$$ F 5

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Publisher
Springer Journals
Copyright
Copyright © 2013 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-013-0620-y
Publisher site
See Article on Publisher Site

Abstract

Self-orthogonal codes with dual distance three and quantum codes with distance three constructed from self-orthogonal codes over $$\mathbb F _5$$ F 5 are discussed in this paper. Firstly, for given code length $$n\ge 5$$ n ≥ 5 , a $$[n,k]_{5}$$ [ n , k ] 5 self-orthogonal code with minimal dimension $$k$$ k and dual distance three is constructed. Secondly, for each $$n\ge 5$$ n ≥ 5 , two nested self-orthogonal codes with dual distance two and three are constructed, and consequently quantum code of length $$n$$ n and distance three is constructed via Steane construction. All of these quantum codes constructed via Steane construction are optimal or near optimal according to the quantum Hamming bound.

Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 10, 2013

References

  • Concatenated quantum codes constructible in polynomial time: efficient decoding and error correction
    Hamada, M

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