Toric codes are examples of evaluation codes produced by evaluating homogeous
polynomials of a fixed degree $\alpha $ at the $\F_q $-rational points of a subset $ Y $ of a …

Toric codes are examples of evaluation codes. They are produced by evaluating
homogeous polynomials of a fixed degree at the F q-rational points of a subset Y of a toric …

Motivated by applications to the theory of error-correcting codes, we give an algorithmic
method for computing a generating set for the ideal generated by β-graded polynomials …

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 …

Motivated by applications to the theory of error-correcting codes, we give an algorithmic
method for computing a generating set for the ideal generated by $\beta $-graded …

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 …

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] …

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 …

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 …

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 …