• DocumentCode
    110093
  • Title

    Propelinear 1-Perfect Codes From Quadratic Functions

  • Author

    Krotov, Denis S. ; Potapov, Vladimir N.

  • Author_Institution
    Sobolev Inst. of Math., Novosibirsk, Russia
  • Volume
    60
  • Issue
    4
  • fYear
    2014
  • fDate
    Apr-14
  • Firstpage
    2065
  • Lastpage
    2068
  • Abstract
    Perfect codes obtained by the Vasil´ev-Schönheim construction from a linear base code and quadratic switching functions are transitive and, moreover, propelinear. This gives at least exp(cN2) propelinear 1-perfect codes of length N over an arbitrary finite field, while an upper bound on the number of transitive codes is exp(C(NlnN)2vphantom)).
  • Keywords
    group codes; linear codes; Vasil´ev-Schonheim construction; arbitrary finite field; linear base code; propelinear 1-perfect codes; quadratic switching functions; transitive codes; Educational institutions; Error correction codes; Propulsion; Space vehicles; Upper bound; Vectors; Perfect code; automorphism group; propelinear code; transitive code;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2014.2303158
  • Filename
    6746188
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=110093