Minimal and maximal arrangements of hyperplanes in \(\mathbb P^{n}(\mathbb {F}_{q})\)

DOI10.1016/j.crma.2007.01.006zbMath1163.14016OpenAlexW196087707MaRDI QIDQ875308

Adnen Sboui, François Rodier

Publication date: 13 April 2007

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2007.01.006

Mathematics Subject Classification ID

Rational points (14G05) Finite ground fields in algebraic geometry (14G15)

Related Items (6)

Bounds on the number of rational points of algebraic hypersurfaces over finite fields, with applications to projective Reed-Muller codes ⋮ On low weight codewords of generalized affine and projective Reed-Muller codes ⋮ The second and the third smallest arrangements of hyperplanes in finite projective spaces ⋮ Maximal hypersurfaces of degree \(d\) in \({{\mathbb{P}}}^n({{\mathbb{F}}}_q)\) and minimum weight spectrum of the generalized \(PRM (q, d, n)\)-code ⋮ On the next-to-minimal weight of projective Reed-Muller codes ⋮ Galois geometries and coding theory

Cites Work

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• The parameters of projective Reed-Müller codes
• Special numbers of rational points on hypersurfaces in the \(n\)-dimensional projective space over a finite field
• On the number of solutions of polynomial systems
• On the number of points of some hypersurfaces in \(\mathbb{F}^n_q\)
• Projective Reed-Muller codes

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