Codes and Elliptic Curves

  • Gerard van der Geer
Part of the Progress in Mathematics book series (PM, volume 94)


In this paper we discuss recent results ([1], [2], [3], [4], [5], [9]) on codes and algebraic curves. We are not concerned with algebraic geometric Goppa codes but rather with another link between coding theory and algebraic geometry. In our case the codes correspond to families of algebraic curves over a finite field, whereas Goppa codes come from a fixed algebraic curve. We use algebraic geometry to determine the weight distributions of certain codes but also we show that results from coding theory may be used to obtain results about the variation of the number of points in families of algebraic curves over a finite field. We do not assume that the reader has a knowledge of coding theory.


Elliptic Curve Finite Field Elliptic Curf Algebraic Curf Cyclic Code 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Gerard van der Geer
    • 1
  1. 1.Faculteit Wiskunde en InformaticaUniversiteit van AmsterdamAmsterdamThe Netherlands

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