Parameterized affine codes

DOI10.1556/SScMath.49.2012.3.1216zbMath1289.13022arXiv1109.2353OpenAlexW2962686509MaRDI QIDQ2859348

Rafael H. Villarreal, Maria Vaz Pinto, Eliseo Sarmiento, Hiram H. López-Valdez

Publication date: 7 November 2013

Published in: Studia Scientiarum Mathematicarum Hungarica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.2353

zbMATH Keywords

dimensionlinear codeslengthminimum distanceevaluation codesvanishing idealsprojective codesaffine Hilbert functionparameterized affine 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 (7)

Direct products in projective Segre codes ⋮ Minimum distance functions of graded ideals and Reed-Muller-type codes ⋮ Complete intersection vanishing ideals on degenerate tori over finite fields ⋮ Evaluation codes and their basic parameters ⋮ Minimum distance functions of complete intersections ⋮ The dual of an evaluation code ⋮ The Degree and Regularity of Vanishing Ideals of Algebraic Toric Sets Over Finite Fields

Uses Software

• Macaulay2

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