Toric Codes over Finite Fields
Applicable Algebra in Engineering, Communication and Computing
On toric codes and multivariate Vandermonde matrices
Applicable Algebra in Engineering, Communication and Computing
Toric Surface Codes and Minkowski Sums
SIAM Journal on Discrete Mathematics
On the parameters of r-dimensional toric codes
Finite Fields and Their Applications
The Order Bound for Toric Codes
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Small polygons and toric codes
Journal of Symbolic Computation
Weighted Reed---Muller codes revisited
Designs, Codes and Cryptography
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Toric codes are obtained by evaluating rational functions of a nonsingular toric variety at the algebraic torus. One can extend toric codes to the so-called generalized toric codes. This extension consists of evaluating elements of an arbitrary polynomial algebra at the algebraic torus instead of a linear combination of monomials whose exponents are rational points of a convex polytope. We study their multicyclic and metric structure, and we use them to express their dual and to estimate their minimum distance.