Highest numbers of points of hypersurfaces over finite fields and generalized Reed-Muller codes

DOI10.1016/j.ffa.2008.02.001zbMath1175.94126OpenAlexW1992195618MaRDI QIDQ938777

Adnen Sboui, François Rodier

Publication date: 27 August 2008

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2008.02.001

zbMATH Keywords

weightsReed-Muller codeshypersurfaceshyperplane arrangements

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Curves over finite and local fields (11G20) Hypersurfaces and algebraic geometry (14J70)

Related Items (7)

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 ⋮ On the next-to-minimal weight of projective Reed-Muller codes ⋮ A study of intersections of quadrics having applications on the small weight codewords of the functional codes \(C_2(Q)\), \(Q\) a non-singular quadric ⋮ On two upper bounds for hypersurfaces involving a Thas' invariant ⋮ On a Homma-Kim conjecture for nonsingular hypersurfaces

Cites Work

• 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 points of some hypersurfaces in \(\mathbb{F}^n_q\)
• Plane curves with many points over finite fields
• Second highest number of points of hypersurfaces in \(\mathbb F_q^n\)
• Projective Reed-Muller codes
• Unnamed Item

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