Binary spherical geometric codes

  • Marc Perret
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 539)


Let q be a power of an odd prime number and Fq be the finite field with q elements. We will construct a binary spherical code from an algebraic curve C defined over Fq and a rational divisor G on C, as the twist by the quadratic character η of the Goppa code L(G). The computation of the parameters of this code is based on the study of some character sums.


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  1. [1]
    Conway, J. H. and Sloane, N. J. A. "Sphere packing, Lattices and Groups", Springer-Verlag, New-York, 1988.Google Scholar
  2. [2]
    Perret, M. "Multiplicative character sums and Kummer coverings", Acta Arithmetica, 59 no3 (1991), p. 75–86.Google Scholar
  3. [3]
    Perret, M. "Multiplicative character sums and non linear geometric codes", symposia of Eurocode 90, to appear in Lecture Notes in Computer Sciences, Springer.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Marc Perret
    • 1
  1. 1.Equipe C.N.R.S. “Arithmétique & Théorie de l'information”Marseille Cedex 9France

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