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 …

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

This work is a natural continuation of our previous work [14]. In this paper, we give a
complete classification of toric surface codes of dimension equal to 6, except a special pair …

This is an addendum to the beautiful paper by Little and Schwarz (Appl Algebra Eng
Commun Comput 18: 349–367, 2007) in which one case of toric surface codes of dimension …

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 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] …

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 …

In this paper, we provide a technique to bound below the minimum distance of a toric code
based on a three dimensional lattice polytope. We also fully classify three dimensional …

The authors expand the results of J. Hansen and give two more toric surface codes,
calculate the dimension of the code by using the methods of cohomology and estimate the …

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 …