ON THE VANISHING IDEAL OF AN ALGEBRAIC TORIC SET AND ITS PARAMETRIZED LINEAR CODES

DOI10.1142/S0219498812500727zbMath1252.13019arXiv1107.4284OpenAlexW2963186008MaRDI QIDQ2909802

Rafael H. Villarreal, Eliseo Sarmiento, Maria Vaz Pinto

Publication date: 6 September 2012

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.4284

zbMATH Keywords

complete intersectionslinear codesalgebraic invariantsdegree complexityvanishing ideals

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Finite ground fields in algebraic geometry (14G15) Applications to coding theory and cryptography of arithmetic geometry (14G50) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items (9)

Complete intersection vanishing ideals on degenerate tori over finite fields ⋮ Vanishing ideals over complete multipartite graphs ⋮ Vanishing ideals of parameterized subgroups in a toric variety ⋮ Complete intersection vanishing ideals on sets of clutter type over finite fields ⋮ The minimum distance of parameterized codes on projective tori ⋮ Computing the degree of a lattice ideal of dimension one ⋮ Codes over a weighted torus ⋮ The Degree and Regularity of Vanishing Ideals of Algebraic Toric Sets Over Finite Fields ⋮ Vanishing Ideals Over Graphs and Even Cycles

Uses Software

• Macaulay2

Cites Work

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• The minimum distance of parameterized codes on projective tori
• Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields
• Rees cones and monomial rings of matroids
• Hilbert functions of graded algebras
• The integral closure of subrings associated to graphs
• Relative volumes and minors in monomial subrings.
• Cayley-Bacharach and evaluation codes on complete intersections
• Toric codes over finite fields
• Binomial ideals
• Combinatorial Optimization
• Total dual integrality implies local strong unimodularity
• Projective Reed-Muller codes
• The Geometry of Syzygies
• On generalized ReedMuller codes and their relatives
• Reed-Muller codes on complete intersections.

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