  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.
