Around Sziklai's conjecture on the number of points of a plane curve over a finite field

Authors:
Masaaki Homma;Seon Jeong Kim
Affiliations:
Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan;Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
Venue:
Finite Fields and Their Applications
Year:
2009

Citing 2
Cited 2

Designs and their codes

Designs and their codes
A bound on the number of points of a plane curve

Finite Fields and Their Applications

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

Finite Fields and Their Applications
Sziklai's conjecture on the number of points of a plane curve over a finite field III

Finite Fields and Their Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper has double purposes. One of them is to give a new bound on the number of points of a plane curve of degree d over a finite field that meets Sziklai's conjectural bound at d=q+1. An example shows that this bound is sharp for d=q+1. The second one is to study an example against that conjecture for q=d=4. This curve also shows the sharpness of our bound.