• DocumentCode
    1257476
  • Title

    The Automorphism Group of a Self-Dual [72, 36, 16] Binary Code Does Not Contain Elements of Order 6

  • Author

    Borello, Martino

  • Author_Institution
    Dipt. di Mat. e Applicazioni, Univ. degli Studi di Milano Bicocca, Milan, Italy
  • Volume
    58
  • Issue
    12
  • fYear
    2012
  • Firstpage
    7240
  • Lastpage
    7245
  • Abstract
    The existence of an extremal code of length 72 is a long-standing open problem. Let C be a putative extremal code of length 72 and suppose that C has an automorphism g of order 6. We show that C, as an BBF2〈g〉 -module, is the direct sum of two modules; it is easy to determine one of them, while the other one has a very restrictive structure. We use this fact to do an exhaustive search and we do not find an extremal code. This proves that the automorphism group of an extremal code of length 72 does not contain elements of order 6.
  • Keywords
    binary codes; dual codes; automorphism group; extremal code; putative extremal code; self-dual [72, 36, 16] binary code; Binary codes; Generators; Linear code; Vectors; Automorphism group; extremal code;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2012.2211095
  • Filename
    6257489
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1257476