Group codes on certain algebraic curves with many rational points

  • Johan P. Hansen
  • Henning Stichtenoth
Article

Abstract

We construct a series of algebraic geometric codes using a class of curves which have many rational points. We obtain codes of lengthq2 over\(\mathbb{F}\) q , whereq = 2q 0 2 andq0 = 2 n , such that dimension + minimal distance ≧q2 + 1 − q0(q − 1). The codes are ideals in the group algebra\(\mathbb{F}\) q [S], whereS is a Sylow-2-subgroup of orderq2 of the Suzuki-group of orderq2(q2 + 1)(q − 1). The curves used for construction have in relation to their genera the maximal number of\(\mathbb{F}\) GF q -rational points. This maximal number is determined by the explicit formulas of Weil and is effectively smaller than the Hasse—Weil bound.

Keywords

Group codes Algebraic function fields Rational points on curves over finite fields Algebraic geometric codes 

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Johan P. Hansen
    • 1
  • Henning Stichtenoth
    • 2
  1. 1.Matematisk InstitutAarhus UniversitetAarhus CDK-Denmark
  2. 2.Universität GHS Essen, Fachbereich 6-MathematikEssen 1FRG

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