On the vanishing ideal of an algebraic toric set and its parameterized linear codes

Abstract

Let K be a finite field and let X be a subset of a projective space, over the field K, which is parameterized by monomials arising from the edges of a clutter. We show some estimates for the degree-complexity, with respect to the revlex order, of the vanishing ideal I(X) of X. If the clutter is uniform, we classify the complete intersection property of I(X) using linear algebra. We show an upper bound for the minimum distance of certain parameterized linear codes along with certain estimates for the algebraic invariants of I(X).

J. Algebra Appl., to appear

Cited by in corpus (2)

• Complete intersection vanishing ideals on degenerate tori over finite fields
• Complete intersection vanishing ideals on sets of clutter type over finite fields