TY - JOUR
T1 - On the vanishing ideal of an algebraic toric set and its parametrized linear codes
AU - Sarmiento, Eliseo
AU - Pinto, Maria Vaz
AU - Villarreal, Rafael H.
N1 - Funding Information:
We thank Hiram López and Carlos Rentería for many stimulating discussions. We also thank the referees for their careful reading of the paper and for the improvements that they suggested. The first author was partially supported by CONACyT. The second author is a member of the Center for Mathematical Analysis, Geometry and Dynamical Systems. The third author was partially supported by CONACyT grant 49251-F and SNI.
PY - 2012/8
Y1 - 2012/8
N2 - Let K be a finite field and let X be a subset of a projective space, over the field K, which is parametrized 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 parametrized linear codes along with certain estimates for the algebraic invariants of I(X).
AB - Let K be a finite field and let X be a subset of a projective space, over the field K, which is parametrized 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 parametrized linear codes along with certain estimates for the algebraic invariants of I(X).
KW - Complete intersections
KW - algebraic invariants
KW - degree complexity
KW - linear codes
KW - vanishing ideals
UR - http://www.scopus.com/inward/record.url?scp=84864349330&partnerID=8YFLogxK
U2 - 10.1142/S0219498812500727
DO - 10.1142/S0219498812500727
M3 - Artículo
SN - 0219-4988
VL - 11
JO - Journal of Algebra and its Applications
JF - Journal of Algebra and its Applications
IS - 4
M1 - 1250072
ER -