The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Algebraic-Geometric Codes
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
Toric Surface Codes and Minkowski Length of Polygons
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
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This paper is concerned with the minimum distance computation for higher dimensional toric codes defined by lattice polytopes in $\mathbb{R}^n$. We show that the minimum distance is multiplicative with respect to taking the product of polytopes, and behaves in a simple way when one builds a $k$-dilate of a pyramid over a polytope. This allows us to construct a large class of examples of higher dimensional toric codes where we can compute the minimum distance explicitly.