Maximal curves with respect to quadratic extensions over finite fields
Abstract
In this paper, we propose a detailed study of a canonical bound which relates the numbers of rational points of a curve over a finite field with that over its quadratic extension. Alternative proofs which make a connection with the variance enable to obtain optimal refinements. [Formula: see text]We focus on the curves reaching the bound, which we call Hallouin–Perret-maximal curves. We provide different characterizations and stress natural links with the curves which attain the Ihara bound. As consequences, we establish the list of such curves with low genus and we outline a maximality result which involves the Suzuki curves. [Formula: see text]At last, we determine which polynomials correspond to the Jacobian of a Hallouin–Perret-maximal curve of genus 2.
Fields of Study & Subjects
advanced mathematical theories
Cryptography and Residue Arithmetic
Publication details
- Journal / source
- International Journal of Number Theory
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 22
- Issue
- 10
- Pages
- 1–27
- Publication date
- 22 May 2026
- Language
- EN