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 …

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 …

Let X be a complete simplicial toric variety over a finite field F q with homogeneous
coordinate ring S= F q [x 1,…, xr] and split torus TX≅(F q⁎) n. We prove that submonoids of …

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 …

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 …

For any integral convex polytope in ℝ there is an explicit construction of an error-correcting
code of length (q-1) 2 over the finite field 𝔽 q, obtained by evaluation of rational functions on …

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 …

In this paper we construct evaluation codes on zero-dimensional complete intersections in
toric varieties and give lower bounds for their minimum distance. This generalizes the results …

In this note, a class of error-correcting codes is associated to a toric variety defined over a
finite field q, analogous to the class of AG codes associated to a curve. For small q, many of …

Let X be a complete n-dimensional simplicial toric variety with homogeneous coordinate ring
S. We study the multigraded Hilbert function HY of reduced 0-dimensional subschemes Y in …