Maximal hypersurfaces of degree \(d\) in \({{\mathbb{P}}}^n({{\mathbb{F}}}_q)\) and minimum weight spectrum of the generalized \(PRM (q, d, n)\)-code

DOI10.1007/s00022-024-00713-wOpenAlexW4392282744MaRDI QIDQ6131541

Adnen Sboui

Publication date: 5 April 2024

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-024-00713-w

zbMATH Keywords

Reed-Muller codeshomogeneous polynomialsprojective hypersurfacesfinite fields \({{\mathbb{F}}}_q\)

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Hypersurfaces and algebraic geometry (14J70)

Cites Work

• Minimal and maximal arrangements of hyperplanes in \(\mathbb P^{n}(\mathbb {F}_{q})\)
• The parameters of projective Reed-Müller codes
• Special numbers of rational points on hypersurfaces in the \(n\)-dimensional projective space over a finite field
• Linear codes and modular curves
• Projective Reed-Muller codes
• New generalizations of the Reed-Muller codes--I: Primitive codes
• On generalized ReedMuller codes and their relatives
• Unnamed Item

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