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 …

Toric codes are a class of m-dimensional cyclic codes introduced recently by Hansen
(Coding theory, cryptography and related areas (Guanajuato, 1998), pp 132–142, Springer …

In this paper we discuss combinatorial questions about lattice polytopes motivated by recent
results on minimum distance estimation for toric codes. We also include a new inductive …

The Order Bound for Toric Codes Page 1 The Order Bound for Toric Codes Peter Beelen and
Diego Ruano ⋆ DTU-Mathematics, Technical University of Denmark, Matematiktorvet, Building …

This work is a natural continuation of our previous work [14]. In this paper, we give a
complete classification of toric surface codes of dimension equal to 6, except a special pair …

This paper is concerned with the minimum distance computation for higher dimensional toric
codes defined by lattice polytopes in R^n. We show that the minimum distance is …

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 …

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 …

We describe two different approaches to making systematic classifications of plane lattice
polygons, and recover the toric codes they generate, over small fields, where these match or …