Computing with toric varieties
Journal of Symbolic Computation
On the structure of generalized toric codes
Journal of Symbolic Computation
The Order Bound for Toric Codes
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Bringing Toric Codes to the Next Dimension
SIAM Journal on Discrete Mathematics
On the parameters of r-dimensional toric codes
Finite Fields and Their Applications
Toric complete intersection codes
Journal of Symbolic Computation
Small polygons and toric codes
Journal of Symbolic Computation
Weighted Reed---Muller codes revisited
Designs, Codes and Cryptography
Designs, Codes and Cryptography
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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.