The second and the third smallest arrangements of hyperplanes in finite projective spaces

DOI10.1016/j.ffa.2015.10.001zbMath1402.11098OpenAlexW2123975382MaRDI QIDQ897334

Daniele Bartoli, Storme, L.

Publication date: 17 December 2015

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2015.10.001

zbMATH Keywords

Reed-Muller codesrational pointshyperplanes arrangements\((k, 3)\)-arcs

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Blocking sets, ovals, (k)-arcs (51E21) Varieties over finite and local fields (11G25)

Cites Work

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• Second weight codewords of generalized Reed-Muller codes
• On low weight codewords of generalized affine and projective Reed-Muller codes
• Minimal and maximal arrangements of hyperplanes in \(\mathbb P^{n}(\mathbb {F}_{q})\)
• The parameters of projective Reed-Müller codes
• Highest numbers of points of hypersurfaces over finite fields and generalized Reed-Muller codes
• On the second weight of generalized Reed-Muller codes
• Special numbers of rational points on hypersurfaces in the \(n\)-dimensional projective space over a finite field
• Nonsingular plane cubic curves over finite fields
• On the number of rational points on codimension 1 algebraic sets in \(\mathbb{P}^ n (\mathbb{F}_ q)\)
• On plane arcs contained in cubic curves
• Second highest number of points of hypersurfaces in \(\mathbb F_q^n\)
• The second weight of generalized Reed-Muller codes in most cases
• Projective Reed-Muller codes
• Abelian varieties over finite fields

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