The uniqueness of a plane curve of degree \(q\) attaining Sziklai's bound over \(\mathbb F_{q}\)

DOI10.1016/j.ffa.2011.12.002zbMath1243.14024OpenAlexW2038627873MaRDI QIDQ413559

Masaaki Homma, Seon Jeong Kim

Publication date: 7 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2011.12.002

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 (3)

Fragments of plane filling curves of degree \(q + 2\) over the finite field of \(q\) elements, and of affine-plane filling curves of degree \(q + 1\) ⋮ Optimal plane curves of degree \(q - 1\) over a finite field ⋮ Numbers of points of surfaces in the projective 3-space over finite fields

Cites Work

• Toward determination of optimal plane curves with a fixed degree over a finite field
• 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
• Nonsingular plane cubic curves over finite fields
• 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
• Unnamed Item
• Unnamed Item

This page was built for publication: The uniqueness of a plane curve of degree \(q\) attaining Sziklai's bound over \(\mathbb F_{q}\)