• DocumentCode
    1230782
  • Title

    On Z4-duality

  • Author

    Carlet, Claude

  • Volume
    41
  • Issue
    5
  • fYear
    1995
  • fDate
    9/1/1995 12:00:00 AM
  • Firstpage
    1487
  • Lastpage
    1494
  • Abstract
    Recently the notion on binary codes called Z4-linearity was introduced. This notion explains why Kerdock codes and Delsarte-Goethals codes admit formal duals in spite of their nonlinearity. The “Z4-duals” of these codes (called “Preparata” and “Goethals” codes) are new nonlinear codes which admit simpler decoding algorithms than the previously known formal duals (the generalized Preparata and Goethals codes). We prove, by using the notion of exact weight enumerator, that the relationship between any Z4-linear code and its Z4 -dual is stronger than the standard formal duality and we deduce the weight enumerators of related generalized codes
  • Keywords
    decoding; dual codes; error correction codes; linear codes; Delsarte-Goethals codes; Goethals codes; Kerdock codes; Preparata codes; Z4-duality; Z4-linearity; binary codes; decoding algorithms; error correcting codes; exact weight enumerator; formal duals; generalized codes; nonlinear codes; nonlinearity; Binary codes; Code standards; Computer science; Decoding; Error correction codes; Galois fields; Graph theory; Hamming weight; Linear code; Polynomials;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.412694
  • Filename
    412694
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1230782