Optimal curves of genus 1,2 and 3
Christophe Ritzenthaler
TL;DR
This survey explores the maximum number of rational points on algebraic curves of genus 1, 2, and 3 over finite fields, summarizing known results and open problems in the area.
Contribution
It provides a comprehensive overview of the current state of knowledge regarding point counts on low-genus curves over finite fields.
Findings
Summarizes known maximum point counts for genus 1, 2, and 3 curves.
Identifies open problems and conjectures in the field.
Highlights recent advances and techniques used in the study.
Abstract
In this survey, we discuss the problem of the maximum number of points of curves of genus 1,2 and 3 over finite fields
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Taxonomy
TopicsCoding theory and cryptography · Cryptography and Residue Arithmetic · Limits and Structures in Graph Theory