On the vanishing ideal of an algebraic toric set and its parameterized   linear codes
  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). 
Eliseo Sarmiento, Maria Vaz Pinto, Rafael H. Villarreal
math.AC math.AG