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 …

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 …

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 …

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 …

Let S be a set of arbitrary objects, and let S d={v 1... vd: vi∈ S}. A polybox code is a set V⊂ S
d with the property that for every two words v, w∈ V there is i∈[d] with vi′= wi, where a …

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 …

Let Fq={0, 1,..., q− 1} be an alphabet of size q, so that Fn q is the q-ary hypercube of
dimension n. Let x=(x1,..., xn) and y=(y1,..., yn) be two elements in Fn q. The Lee distance …

The approach of Kalai and Kahn towards counterexamples of Borsuk's conjecture is
generalized to spherical codes. This allows the construction of a finite set in R 323 which …

We describe odd-length-cube tilings of the n-dimensional q-ary torus what includes q-
periodic integer lattice tilings of R^ n. In the language of coding theory these tilings …