The theory of affine geometries over the rings Z/< q− 1> can be used to understand the
properties of toric and generalized toric codes over F q. The standard generator matrices of …

Advances in Algebraic Geometry Codes : Toric Codes Page 1 Chapter 8 Toric Codes Edgar
Martınez-Moro and Diego Ruano∗ Departamento de Matemática Aplicada, Universidad de …

Toric codes are obtained by evaluating rational functions of a nonsingular toric variety at the
algebraic torus. One can extend toric codes to the so-called generalized toric codes. This …

Let X be a complete simplicial toric variety over a finite field with a split torus TX. For any
matrix Q, we are interested in the subgroup YQ of TX parameterized by the columns of Q. We …

Let X be a complete simplicial toric variety over a finite field F q with homogeneous
coordinate ring S= F q [x 1,…, xr] and split torus TX≅(F q⁎) n. We prove that submonoids of …

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⊂ R 2 varies with the base …

In this note, a class of error-correcting codes is associated to a toric variety defined over a
finite field q, analogous to the class of AG codes associated to a curve. For small q, many of …

J. Hansen introduced toric codes using the geometry of polygons in R2 and the convex
polytopes P in Rm more generally. But collections of points more general than the sets P∩ …

Toric codes are a class of $ m $-dimensional cyclic codes introduced recently by J. Hansen.
They may be defined as evaluation codes obtained from monomials corresponding to …

From a rational convex polytope of dimension r⩾ 2 JP Hansen constructed an error
correcting code of length n=(q− 1) r over the finite field Fq. A rational convex polytope is the …