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A Geometric View of Decoding AG Codes

  • Thanasis Bouganis
  • Drue Coles
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2643)

Abstract

We investigate the use of vector bundles over finite fields to obtain a geometric view of decoding algebraic-geometric codes. Building on ideas of Trygve Johnsen, who revealed a connection between the errors in a received word and certain vector bundles on the underlying curve, we give explicit constructions of the relevant geometric objects and efficient algorithms for some general computations needed in the constructions. The use of vector bundles to understand decoding as a geometric process is the first application of these objects to coding theory.

Keywords

Vector Bundle Line Bundle Local Parameter Linear Code Parity Check Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Thanasis Bouganis
    • 1
  • Drue Coles
    • 2
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeUK
  2. 2.Computer Science DepartmentBoston UniversityUSA

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