Algebraic-Geometric Codes
Toric Codes over Finite Fields
Applicable Algebra in Engineering, Communication and Computing
Toric Surface Codes and Minkowski Sums
SIAM Journal on Discrete Mathematics
Error-Correcting Codes from Higher-Dimensional Varieties
Finite Fields and Their Applications
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
Algebraic geometry codes from polyhedral divisors
Journal of Symbolic Computation
Bringing Toric Codes to the Next Dimension
SIAM Journal on Discrete Mathematics
Toric complete intersection codes
Journal of Symbolic Computation
Weighted Reed---Muller codes revisited
Designs, Codes and Cryptography
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From a rational convex polytope of dimension r=2 J.P. Hansen constructed an error correcting code of length n=(q-1)^r over the finite field F"q. A rational convex polytope is the same datum as a normal toric variety and a Cartier divisor. The code is obtained evaluating rational functions of the toric variety defined by the polytope at the algebraic torus, and it is an evaluation code in the sense of Goppa. We compute the dimension of the code using cohomology. The minimum distance is estimated using intersection theory and mixed volumes, extending the methods of J.P. Hansen for plane polytopes. Finally we give counterexamples to Joyner's conjectures [D. Joyner, Toric codes over finite fields, Appl. Algebra Engrg. Comm. Comput. 15 (2004) 63-79].