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, introduced by Hansen, are the natural extensions of Reed–Solomon codes. A
toric code is a k-dimensional subspace of 𝔽 qn determined by a toric variety or its associated …

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 …

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 …

Soprunov and Soprunova posed a question on the existence of infinite families of toric
codes that are “good” in a precise sense. We prove that such good families do not exist by …

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 …

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 …

In 1998, JP Hansen introduced the construction of an error-correcting code over a finite field
[special characters omitted] from a convex integral polytope in [special characters omitted] …

Toric codes are examples of evaluation codes produced by evaluating homogeous
polynomials of a fixed degree $\alpha $ at the $\F_q $-rational points of a subset $ Y $ of a …