• DocumentCode
    1502270
  • Title

    Cyclic codes and self-dual codes over F2+uF2

  • Author

    Bonnecaze, A. ; Udaya, P.

  • Author_Institution
    GECT, Toulon Univ., La Garde, France
  • Volume
    45
  • Issue
    4
  • fYear
    1999
  • fDate
    5/1/1999 12:00:00 AM
  • Firstpage
    1250
  • Lastpage
    1255
  • Abstract
    We introduce linear cyclic codes over the ring F2+uF 2={0,1,u,u¯=u+1}, where u2=0 and study them by analogy with the Z4 case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z4-codes. Unlike the Z4 case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-dual codes through a linear Gray map
  • Keywords
    binary codes; cyclic codes; dual codes; linear codes; Z4-codes; alphabet; code structure; extremal self-dual codes; free codes; integer rings; linear Gray map; linear cyclic codes; nonfree codes; odd length code; optimal binary linear codes; self-dual codes; Binary codes; Cities and towns; Galois fields; Information theory; Lattices; Linear code; Mathematics; Modular construction; Polynomials; Reactive power;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.761278
  • Filename
    761278
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1502270