• DocumentCode
    1355916
  • Title

    Surfaces and the weight distribution of a family of codes

  • Author

    van der Vlugt, M.

  • Author_Institution
    Dept. of Math. & Comput. Sci., Leiden Univ., Netherlands
  • Volume
    43
  • Issue
    4
  • fYear
    1997
  • fDate
    7/1/1997 12:00:00 AM
  • Firstpage
    1354
  • Lastpage
    1360
  • Abstract
    We derive the weight distribution of the binary trace codes with words (Tr(axq+1+bx3+cx))x∈F*(q2) where a, b, c∈F(q2) and Tr is the trace map from F(q2) to F2. The weights of these words determine the exponential sums which were considered earlier by Moreno and Kumar (1994) and Lahtonen (1995). Results from the theory of quadratic forms play a role but the decisive argument is of an algebraic-geometric nature, namely, from the theory of surfaces
  • Keywords
    algebraic geometric codes; binary sequences; cyclic codes; algebraic-geometric nature; binary trace codes; exponential sums; quadratic forms; theory of surfaces; trace map; weight distribution; Equations; Error correction codes; Galois fields; Geometry; H infinity control; Information theory; Upper bound;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.605608
  • Filename
    605608
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1355916