Vanishing ideals over complete multipartite graphs

DOI10.1016/j.jpaa.2013.11.005zbMath1443.13019arXiv1302.0734OpenAlexW2963115675MaRDI QIDQ393520

Maria Vaz Pinto, Jorge Neves

Publication date: 23 January 2014

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.0734

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Linear codes (general theory) (94B05) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) 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) Commutative rings defined by binomial ideals, toric rings, etc. (13F65)

Related Items (9)

The second generalized Hamming weight of some evaluation codes arising from a projective torus ⋮ Parameterized codes associated to the edges of some subgraphs of a simple graph ⋮ Joins, ears and Castelnuovo-Mumford regularity ⋮ Generalized Hamming weights and some parameterized codes ⋮ Parameterized codes over graphs ⋮ Regularity of the vanishing ideal over a parallel composition of paths ⋮ Regularity of the vanishing ideal over a bipartite nested ear decomposition ⋮ Codes over a weighted torus ⋮ Symbolic powers of certain cover ideals of graphs

Cites Work

• Complete intersection vanishing ideals on degenerate tori over finite fields
• The minimum distance of parameterized codes on projective tori
• Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields
• Hilbert functions of graded algebras
• Linkage and codes on complete intersections
• Binomial ideals
• COMPLETE INTERSECTIONS IN BINOMIAL AND LATTICE IDEALS
• ON THE VANISHING IDEAL OF AN ALGEBRAIC TORIC SET AND ITS PARAMETRIZED LINEAR CODES
• Cayley-Bacharach Schemes and Their Canonical Modules
• Rees algebras of edge ideals
• Reed-Muller codes on complete intersections.
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