Parameterized affine codes
Commutative Algebra
2024-02-07 v2 Algebraic Geometry
Abstract
Let K be a finite field and let X* be an affine algebraic toric set parameterized by monomials. We give an algebraic method, using Groebner bases, to compute the length and the dimension of C_X*(d), the parameterized affine code of degree d on the set X*. If Y is the projective closure of X*, it is shown that C_X^*(d) has the same basic parameters that C_Y(d), the parameterized projective code on the set Y. If X* is an affine torus, we compute the basic parameters of C_X*(d). We show how to compute the vanishing ideals of X* and Y.
Keywords
Cite
@article{arxiv.1109.2353,
title = {Parameterized affine codes},
author = {Hiram H. Lopez and Eliseo Sarmiento and Maria Vaz Pinto and Rafael H. Villarreal},
journal= {arXiv preprint arXiv:1109.2353},
year = {2024}
}
Comments
Studia Sci. Math. Hungar., to appear