English

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

R2 v1 2026-06-21T19:03:14.450Z