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Toric Codes over Finite Fields

  • David Joyner
Article

Abstract.

In this note, a class of error-correcting codes is associated to a toric variety defined over a finite field Open image in new window q , analogous to the class of AG codes associated to a curve. For small q, many of these codes have parameters beating the Gilbert-Varshamov bound. In fact, using toric codes, we construct a (n,k,d)=(49,11,28) code over Open image in new window 8, which is better than any other known code listed in Brouwer’s tables for that n, k and q. We give upper and lower bounds on the minimum distance. We conclude with a discussion of some decoding methods. Many examples are given throughout.

Keywords

AG codes Toric varieties Reed-Muller codes 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Math DeptUS Naval AcademyUSA

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