• DocumentCode
    1502221
  • Title

    Upper bounds on the size of quantum codes

  • Author

    Ashikhmin, Alexei ; Litsyu, S.

  • Author_Institution
    Los Alamos Nat. Lab., NM, USA
  • Volume
    45
  • Issue
    4
  • fYear
    1999
  • fDate
    5/1/1999 12:00:00 AM
  • Firstpage
    1206
  • Lastpage
    1215
  • Abstract
    This paper is concerned with bounds for quantum error-correcting codes. Using the quantum MacWilliams (1972, 1977) identities, we generalize the linear programming approach from classical coding theory to the quantum case. Using this approach, we obtain Singleton-type, Hamming-type, and the first linear-programming-type bounds for quantum codes. Using the special structure of linear quantum codes, we derive an upper bound that is better than both Hamming and the first linear programming bounds on some subinterval of rates
  • Keywords
    error correction codes; linear codes; linear programming; quantum cryptography; Hamming-type bound; Singleton-type bound; classical coding theory; code rates; code size; first linear programming bound; linear quantum codes; quantum MacWilliams identities; quantum error-correcting codes; upper bound; upper bounds; Application software; Computer errors; Error correction codes; Linear programming; Polynomials; Protection; Quantum computing; Quantum mechanics; Rain; Upper bound;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.761270
  • Filename
    761270