• DocumentCode
    1369888
  • Title

    The Perfect Binary One-Error-Correcting Codes of Length 15 : Part I—Classification

  • Author

    Ostergard, P. ; Pottonen, O.

  • Author_Institution
    Dept. of Commun. & Networking, Helsinki Univ. of Technol. TKK, Helsinki, Finland
  • Volume
    55
  • Issue
    10
  • fYear
    2009
  • Firstpage
    4657
  • Lastpage
    4660
  • Abstract
    A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 is presented. There are 5983 such inequivalent perfect codes and 2165 extended perfect codes. Efficient generation of these codes relies on the recent classification of Steiner quadruple systems of order 16. Utilizing a result of Blackmore, the optimal binary one-error-correcting codes of length 14 and the (15, 1024, 4) codes are also classified; there are 38 408 and 5983 such codes, respectively.
  • Keywords
    Hamming codes; binary codes; error correction codes; Hamming code; Steiner quadruple systems; binary one-error-correcting codes; Automation; Binary codes; Electronic mail; Classification; Hamming code; Steiner system; perfect binary code;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2009.2027525
  • Filename
    5238744
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1369888