Homogeneous polynomials vanishing on the projective space \(\mathbb{P}^m(\mathbb{F}_q)\)

DOI10.1016/S0022-4049(96)00104-1zbMath0899.13028OpenAlexW2082121337MaRDI QIDQ1380015

Robert Rolland, Dany-Jack Mercier

Publication date: 25 February 1998

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

Full work available at URL: https://doi.org/10.1016/s0022-4049(96)00104-1

zbMATH Keywords

free resolutionhomogeneous polynomials

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linkage, complete intersections and determinantal ideals (13C40) Finite fields (field-theoretic aspects) (12E20) Polynomials and finite commutative rings (13M10)

Related Items (14)

Number of solutions of systems of homogeneous polynomial equations over finite fields ⋮ On low weight codewords of generalized affine and projective Reed-Muller codes ⋮ The saturation number of monomial ideals ⋮ On the next-to-minimal weight of projective Reed-Muller codes ⋮ Saturation and vanishing ideals ⋮ Subfield subcodes of projective Reed-Muller codes ⋮ A Combinatorial Approach to the Number of Solutions of Systems of Homogeneous Polynomial Equations over Finite Fields ⋮ Evaluation codes and their basic parameters ⋮ Towards the complete determination of next-to-minimal weights of projective Reed-Muller codes ⋮ Vanishing ideals of projective spaces over finite fields and a projective footprint bound ⋮ Generalized minimum distance functions ⋮ A note on Nullstellensatz over finite fields ⋮ Group structure on projective spaces and cyclic codes over finite fields ⋮ Reed-Muller-type codes over the Segre variety

Cites Work

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• The parameters of projective Reed-Müller codes
• Equations et variétés algébriques sur un corps fini
• Ideals defined by matrices and a certain complex associated with them
• Projective Reed-Muller codes
• Torsions Quadratiques et Bases Normales Autoduales
• On generalized ReedMuller codes and their relatives

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