Bringing Toric Codes to the next dimension

Details Bringing Toric Codes to the next dimension Bringing Toric Codes to the next dimension

2009-05-07

arxiv.org/abs/0905.1056v2

SIAM J. Discrete Math. Volume 24, no. 2, pp. 655-665 (2010)

Mathematics

Algebraic Geometry

11 pages, 1 figure; Major changes in the section on parameters, new examples.

Scientific paper

This paper is concerned with the minimum distance computation for higher dimensional toric codes defined by lattice polytopes. 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.

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