Rational curves with many rational points over a finite field. (English) Zbl 1317.11059

Fukasawa, Satoru; Homma, Masaaki; Kim, Seon Jeong

Aubry, Yves (ed.) et al., Arithmetic, geometry, cryptography and coding theory. 13th conference on arithmetic, geometry, cryptography and coding theory, CIRM, Marseille, France, March 14–18, 2011 and Geocrypt 2011, Bastia, France, June 19–24, 2011. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-7572-8/pbk; 978-0-8218-9027-1/ebook). Contemporary Mathematics 574, 37-48 (2012).

Summary: We study a particular plane curve over a finite field whose normalization is of genus 0. The number of rational points of this curve achieves the Aubry-Perret bound for rational curves. The configuration of its rational points and a generalization of the curve are also presented.
For the entire collection see [Zbl 1248.11004].

MSC:

11G05	Elliptic curves over global fields
14G15	Finite ground fields in algebraic geometry
14H50	Plane and space curves

Keywords:

plane curve over a finite field; rational points