Hunting for curves with many points
Gerard van der Geer
TL;DR
This paper presents a method for constructing algebraic curves over finite fields that have a large number of rational points by utilizing properties of the class group.
Contribution
The paper introduces a novel approach to generate curves with many points over finite fields leveraging class group structures.
Findings
Successfully constructed curves with record numbers of points
Demonstrated the effectiveness of class group-based methods
Provided new benchmarks for curve point counts
Abstract
We construct curves with many points over finite fields using the class group
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · Polynomial and algebraic computation · semigroups and automata theory