Toward determination of optimal plane curves with a fixed degree over a finite field

DOI10.1016/j.ffa.2010.12.003zbMath1215.14033OpenAlexW2094305993MaRDI QIDQ539898

Masaaki Homma, Seon Jeong Kim

Publication date: 31 May 2011

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2010.12.003

zbMATH Keywords

finite fieldrational pointplane curve

Mathematics Subject Classification ID

Rational points (14G05) Plane and space curves (14H50) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Finite ground fields in algebraic geometry (14G15)

Related Items (5)

Fragments of plane filling curves of degree \(q + 2\) over the finite field of \(q\) elements, and of affine-plane filling curves of degree \(q + 1\) ⋮ The second largest number of points on plane curves over finite fields ⋮ The uniqueness of a plane curve of degree \(q\) attaining Sziklai's bound over \(\mathbb F_{q}\) ⋮ Optimal plane curves of degree \(q - 1\) over a finite field ⋮ Numbers of points of surfaces in the projective 3-space over finite fields

Uses Software

• manYPoints

Cites Work

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• Sziklai's conjecture on the number of points of a plane curve over a finite field. III
• Around Sziklai's conjecture on the number of points of a plane curve over a finite field
• Correction to ``Frobenius non-classical curves
• A bound on the number of points of a plane curve
• Sziklai's conjecture on the number of points of a plane curve over a finite field II
• Weierstrass Points and Curves Over Finite Fields
• Quadratic forms, generalized Hamming weights of codes and curves with many points

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