Abstract.
In this note, a class of error-correcting codes is associated to a toric variety defined over a finite field 
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
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.
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Joyner, D. Toric Codes over Finite Fields. AAECC 15, 63–79 (2004). https://doi.org/10.1007/s00200-004-0152-x
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DOI: https://doi.org/10.1007/s00200-004-0152-x