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 …

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 …

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 …

A toric code, introduced by Hansen to extend the Reed-Solomon code as a $ k $-
dimensional subspace of $\mathbb {F} _q^ n $, is determined by a toric variety or its …

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 …

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 …

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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 …

In this paper we prove new lower bounds for the minimum distance of a toric surface code
C_P defined by a convex lattice polygon P⊂R^2. The bounds involve a geometric invariant …

We define a statistical measure of the typical size of words of low weight in a linear code
over a finite field. We prove that the dual toric codes coming from polytopes of degree one …