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 …

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 …

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 …

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 from Order Polytopes | SpringerLink Skip to main content Advertisement
SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Discrete & …

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 are a specific class of linear codes, originally introduced by J. Hansen [2]. In this
report, we study generalized toric codes, which are generated by a set of points in Zm q− 1 …

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 …

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 …