Vanishing ideals over finite fields

DOI10.1134/S0001434619030131zbMath1420.14112arXiv1502.05451OpenAlexW2963939856MaRDI QIDQ2314109

Rafael H. Villarreal, Azucena Tochimani

Publication date: 19 July 2019

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.05451

zbMATH Keywords

finite fieldrational parametrizationvanishing idealReed-Muller-type code

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Complete intersections (14M10) Finite ground fields in algebraic geometry (14G15)

Related Items (4)

Binomial vanishing ideals ⋮ Minimum distance functions of graded ideals and Reed-Muller-type codes ⋮ Vanishing ideals of parameterized subgroups in a toric variety ⋮ The dual of an evaluation code

Uses Software

• SINGULAR

Cites Work

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• Minimum distance functions of graded ideals and Reed-Muller-type codes
• Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields
• Reed-Muller-type codes over the Segre variety
• Polynomial Interpolation in Several Variables: Lattices, Differences, and Ideals
• Combinatorial Nullstellensatz
• Monomial Algebras

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