Bringing toric codes to the n ext dimension

This paper is concerned with the minimum distance computation for higher dimensional toric codes defined by lattice polytopes in Rn. 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 ak-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. ©2010 Societ y for Industrial and Applied Mathematics.