Remarks on generalized toric codes
Information Theory
2011-09-14 v2 Algebraic Geometry
math.IT
Abstract
This note presents some new information on how the minimum distance of the generalized toric code corresponding to a fixed set of integer lattice points S in R^2 varies with the base field. The main results show that in some cases, over sufficiently large fields, the minimum distance of the code corresponding to a set S will be the same as that of the code corresponding to the convex hull of S. In an example, we will also discuss a [49,12,28] generalized toric code over GF(8), better than any previously known code according to M. Grassl's online tables, as of July 2011.
Cite
@article{arxiv.1107.4530,
title = {Remarks on generalized toric codes},
author = {John B. Little},
journal= {arXiv preprint arXiv:1107.4530},
year = {2011}
}
Comments
14 pages, 4 figures Version 2 corrects some typos, adds a new reference