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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 obtained by evaluating rational functions of a nonsingular toric variety at the
algebraic torus. One can extend toric codes to the so-called generalized toric codes. This …

Any integral convex polytope P in ℝ N provides an N-dimensional toric variety XP and an
ample divisor DP on this variety. This paper gives an explicit construction of the algebraic …

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 …

Tsfasman and Vladut [TV] proposed a general framework of constructing error-correction
codes by using algebraic varieties in their seminal work “Algebraic-Geometry Codes” …

From a rational convex polytope of dimension r⩾ 2 JP Hansen constructed an error
correcting code of length n=(q− 1) r over the finite field Fq. A rational convex polytope is the …

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 …

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 …