COMPLETE INTERSECTIONS IN BINOMIAL AND LATTICE IDEALS

DOI10.1142/S0218196713500288zbMath1291.13034arXiv1205.0772OpenAlexW2168411373MaRDI QIDQ2854966

Rafael H. Villarreal, Hiram H. López-Valdez

Publication date: 24 October 2013

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.0772

zbMATH Keywords

complete intersectiontoric idealsevaluation codesmonomial curvesset theoretic complete intersectionlattices ideals

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Special algebraic curves and curves of low genus (14H45) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items (5)

Complete intersection vanishing ideals on degenerate tori over finite fields ⋮ Minimal generating sets of lattice ideals ⋮ Vanishing ideals over complete multipartite graphs ⋮ Computing the degree of a lattice ideal of dimension one ⋮ Regularity and algebraic properties of certain lattice ideals

Uses Software

• cisimplicial

Cites Work

• The minimum distance of parameterized codes on projective tori
• Binomial generation of the radical of a lattice ideal
• Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields
• Linkage and codes on complete intersections
• Cayley-Bacharach and evaluation codes on complete intersections
• Complete intersection lattice ideals
• On the set-theoretic complete intersection problem for monomial curves in \(\mathbb{A}^ n\) and \(\mathbb{P}^ n\)
• Binomial ideals
• The Horace method for error-correcting codes
• An algorithm for checking whether the toric ideal of an affine monomial curve is a complete intersection
• Generators and relations of abelian semigroups and semigroup rings
• On systems of binomials in the ideal of a toric variety
• Set-theoretic complete intersections on binomials
• Sous-monoïdes d'intersection complète de $N$
• Affine semigroup rings that are complete intersections
• Reed-Muller codes on complete intersections.

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