Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4582963 | Finite Fields and Their Applications | 2013 | 14 Pages |
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⊂R2S⊂R2 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 conv(S)conv(S). In an example, we will also discuss a [49,12,28][49,12,28] generalized toric code over F8F8, better than any previously known code according to M. Grassl's online tables, as of December 2012.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
John B. Little,