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 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 …

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 …

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 …

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 …

Toric surface codes are a class of error-correcting codes coming from a lattice polytope
defining a two-dimensional toric variety. Previous authors have mostly completed …

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 …

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 …

From an integral convex polytope in ℝ 2 we give an explicit description of an error-correcting
code over the finite field\Bbb F _q of length (q—1) 2. The codes are obtained from toric …

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 …