Reed-Muller-type codes over the Segre variety

DOI10.1006/ffta.2002.0360zbMath1020.94029OpenAlexW2026545856MaRDI QIDQ1867464

Horacio Tapia-Recillas, Manuel González Sarabia, Carlos Rentería Márquez

Publication date: 2 April 2003

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/ffta.2002.0360

zbMATH Keywords

minimum distanceprojective Reed-Muller codeSegre variety

Mathematics Subject Classification ID

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)

Related Items (26)

Direct products in projective Segre codes ⋮ Binomial vanishing ideals ⋮ The second generalized Hamming weight of some evaluation codes arising from a projective torus ⋮ Minimum distance functions of graded ideals and Reed-Muller-type codes ⋮ Projective nested Cartesian codes ⋮ Minimum distance of some evaluation codes ⋮ Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields ⋮ Affine Cartesian codes with complementary duals ⋮ Projective Reed-Muller type codes on rational normal scrolls ⋮ Complete intersection vanishing ideals on sets of clutter type over finite fields ⋮ Relative generalized Hamming weights of evaluation codes ⋮ The minimum distance of parameterized codes on projective tori ⋮ Affine Cartesian codes ⋮ Evaluation codes and their basic parameters ⋮ Regularity and algebraic properties of certain lattice ideals ⋮ Minimum distance functions of complete intersections ⋮ Generalized minimum distance functions ⋮ Codes over a weighted torus ⋮ Footprint and minimum distance functions ⋮ Generalized Hamming weights of projective Reed-Muller-type codes over graphs ⋮ Generalized minimum distance functions and algebraic invariants of Geramita ideals ⋮ The dual of an evaluation code ⋮ Linear codes over signed graphs ⋮ Vanishing ideals over finite fields ⋮ Projective Reed-Muller type codes on higher dimensional scrolls ⋮ Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes

Cites Work

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• The \(a\)-invariant of some Reed-Muller codes
• Homogeneous polynomials vanishing on the projective space \(\mathbb{P}^m(\mathbb{F}_q)\)
• Linkage and codes on complete intersections
• The weight hierarchy of product codes
• Reed‐muller codes: an ideal theory approach
• Projective Reed-Muller codes
• On the generalized Hamming weights of product codes
• Reed-Muller codes on complete intersections.

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