A geometric view of decoding AG codes

Authors:
Thanasis Bouganis;Drue Coles
Affiliations:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge;Computer Science Department, Boston University
Venue:
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Year:
2003

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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.