64 citations · 247 across the 16 of their papers we have counts for
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Complete intersection vanishing ideals on degenerate tori over finite fields
Hiram H. Lopez, Rafael H. Villarreal, Leticia Zarate
We study the complete intersection property and the algebraic invariants (index of regularity, degree) of vanishing ideals on degenerate tori over finite fields. We establish a cor…
Computing the degree of a lattice ideal of dimension one
Hiram H. Lopez, Rafael H. Villarreal
We show that the degree of a graded lattice ideal of dimension 1 is the order of the torsion subgroup of the quotient group of the lattice. This gives an efficient method to comput…
Complete intersections in binomial and lattice ideals
Hiram H. Lopez, Rafael H. Villarreal
For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown tha…
Affine cartesian codes
Hiram H. Lopez, Carlos Renteria, Rafael H. Villarreal
We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integer…
Parameterized affine codes
Hiram H. Lopez, Eliseo Sarmiento, Maria Vaz Pinto +1
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 dim…