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Multiplicative character sums and non linear geometric codes

  • Marc Perret
Section 3 Geometric Codes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 514)

Abstract

Let q be a power of a prime number, Fq the finite field with q elements, n an integer dividing q−1, n≥2, and χ a character of order n of the multiplicative group F*q. If X is an algebraic curve defined over Fq and if G is a divisor on X, we define a non linear code Γ(q, X, G, n, χ) on an alphabet with n+1 letters. We compute the parameters of this code, through the consideration of some character sums.

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Bibliography

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Marc Perret
    • 1
  1. 1.Equipe CNRS “Arithmetique & Théorie de l'Information”Marseille Cedex 9France

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