Vanishing Ideals for Codes on Toric Varieties

M Sahin - scale.gtu.edu.tr
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 …

Computing vanishing ideals for Toric codes

M Şahin - arXiv preprint arXiv:2207.01061, 2022 - arxiv.org
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 …

ON THE MINIMUM DISTANCE OF A TORIC CODE VIA VANISHING IDEAL

F Baldemir - 2023 - open.metu.edu.tr
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 …

On the structure of generalized toric codes

D Ruano - Journal of Symbolic Computation, 2009 - Elsevier
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 …

Projective toric codes

J Nardi - International Journal of Number Theory, 2022 - World Scientific
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 …

On parameterized toric codes

E Baran, M Şahin - Applicable Algebra in Engineering, Communication …, 2023 - Springer
Let X be a complete simplicial toric variety over a finite field with a split torus TX. For any
matrix Q, we are interested in the subgroup YQ of TX parameterized by the columns of Q. We …

Toric codes

E Martínez-Moro, D Ruano - Advances in algebraic geometry codes, 2008 - World Scientific
Advances in Algebraic Geometry Codes : Toric Codes Page 1 Chapter 8 Toric Codes Edgar
Martınez-Moro and Diego Ruano∗ Departamento de Matemática Aplicada, Universidad de …

Rational points of lattice ideals on a toric variety and toric codes

M Şahin - Finite Fields and Their Applications, 2023 - Elsevier
We show that the number of rational points of a subgroup inside a toric variety over a finite
field defined by a homogeneous lattice ideal can be computed via Smith normal form of the …

On the parameters of r-dimensional toric codes

D Ruano - Finite Fields and Their Applications, 2007 - Elsevier
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 …

Vanishing ideals of parameterized subgroups in a toric variety

EB Özkan - Turkish Journal of Mathematics, 2022 - journals.tubitak.gov.tr
Let $ K $ be a finite field and $ X $ be a complete simplicial toric variety over $ K $ with split
torus $ T_X\cong (K^*)^ n $. We give an algorithm relying on elimination theory for finding …