Bringing Toric Codes to the next dimension
Algebraic Geometry
2015-06-26 v2 Information Theory
math.IT
Abstract
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.
Cite
@article{arxiv.0905.1056,
title = {Bringing Toric Codes to the next dimension},
author = {Ivan Soprunov and Evgenia Soprunova},
journal= {arXiv preprint arXiv:0905.1056},
year = {2015}
}
Comments
11 pages, 1 figure; Major changes in the section on parameters, new examples.