On a Conjecture of Macwilliams and Sloane

  • F. Rodier
Part of the International Centre for Mechanical Sciences book series (CISM, volume 339)


Let C m be a primitive binary BCH code, of length 2 m − 1 = q −1, and of designed distance δ = 2t + 1. We want to study the dual of this code, which we denote by C m .


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hooley, C.: “On Artin’s conjecture”, J. reine angew. Math., vol. 225 (1967), 209–20.zbMATHMathSciNetGoogle Scholar
  2. 2.
    Lang, S. and Weil, A.: “Number of points of varieties in finite fields”, Amer. J. Math., vol. 76 (1954), 819–827.CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Lidl, R. and Niederreiter, H.: Finite Fields, Encyclopedia of mathematics and its applications, vol. 20, Cambridge University Press, Cambridge, 1983.Google Scholar
  4. 4.
    MacWilliams, F.J. and Sloane, N.J.A.: The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.zbMATHGoogle Scholar
  5. 5.
    Rodier, F.: “On the spectra of the duals of binary BCH codes of designed distance 8 = 9”, IEEE transactions on Information Theory, vol 38, n° 2 (1992), 478–479.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Rodier, F.: “Minoration de certaines sommes exponentielles binaires”, in Coding Theory and Algebraic Geometry(Eds. H. Stichtenoth and M.A. Tsfasman), Lecture Notes in Math. no 1518, Springer-Verlag, 1992.Google Scholar
  7. 7.
    Rodier, F.: “Sur la distance minimale d’un code BCH”, submitted to Discrete Math. (1992).Google Scholar
  8. 8.
    Weil, A.: “On some exponential sums”, Proc. Nat. Acad. Sci. U.S.A., Vol. 34 (1948), 204–207.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • F. Rodier
    • 1
  1. 1.Laboratoire de Mathématiques DiscrètesMarseilleFrance

Personalised recommendations