The minimum distance of parameterized codes on projective tori

DOI10.1007/s00200-011-0148-2zbMath1271.13054arXiv1009.4966OpenAlexW2079254998MaRDI QIDQ429761

Rafael H. Villarreal, Maria Vaz Pinto, Eliseo Sarmiento

Publication date: 20 June 2012

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.4966

zbMATH Keywords

regularitycomplete intersectionsdegreeHilbert functionminimum distanceevaluation codesparameterized codes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) 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)

Related Items (26)

Direct products in projective Segre codes ⋮ The second generalized Hamming weight of some evaluation codes arising from a projective torus ⋮ ON THE VANISHING IDEAL OF AN ALGEBRAIC TORIC SET AND ITS PARAMETRIZED LINEAR CODES ⋮ Minimum distance functions of graded ideals and Reed-Muller-type codes ⋮ Complete intersection vanishing ideals on degenerate tori over finite fields ⋮ Minimum distance of some evaluation codes ⋮ Vanishing ideals over complete multipartite graphs ⋮ Parameterized codes associated to the edges of some subgraphs of a simple graph ⋮ Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields ⋮ Generalized Hamming weights of toric codes over hypersimplices and squarefree affine evaluation codes ⋮ Joins, ears and Castelnuovo-Mumford regularity ⋮ Generalized Hamming weights and some parameterized codes ⋮ Complete intersection vanishing ideals on sets of clutter type over finite fields ⋮ On parameterized toric codes ⋮ Parameterized codes over graphs ⋮ Regularity of the vanishing ideal over a parallel composition of paths ⋮ Bounding invariants of fat points using a coding theory construction ⋮ Affine Cartesian codes ⋮ Computing the degree of a lattice ideal of dimension one ⋮ Evaluation codes and their basic parameters ⋮ Regularity and algebraic properties of certain lattice ideals ⋮ Minimum distance functions of complete intersections ⋮ 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 ⋮ COMPLETE INTERSECTIONS IN BINOMIAL AND LATTICE IDEALS

Cites Work

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• Hilbert functions of graded algebras
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• A note on affine toric varieties
• Cayley-Bacharach and evaluation codes on complete intersections
• Reed-Muller-type codes over the Segre variety
• Binomial ideals
• The Horace method for error-correcting codes
• ON THE VANISHING IDEAL OF AN ALGEBRAIC TORIC SET AND ITS PARAMETRIZED LINEAR CODES
• Reed‐muller codes: an ideal theory approach
• Cayley-Bacharach Schemes and Their Canonical Modules
• Projective Reed-Muller codes
• Combinatorial Nullstellensatz
• The Geometry of Syzygies
• Linear codes associated to the ideal of points in P^dAnd its canonical module
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