We call a polytope terraced if upon projecting onto a one-dimensional coordinate space,
each fiber of the projection is contained in the fiber below it. We present a technique 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 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 …

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Toric codes are evaluation codes obtained from an integral convex polytope P⊂\mathbbR^n
and finite field \mathbbF_q. They are, in a sense, a natural extension of Reed–Solomon …

A toric code is an error-correcting code determined by a toric variety or its associated
integral convex polytope. We investigate $4 $-and $5 $-dimensional toric $3 $-fold codes …

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 …

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 …

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 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 …