How to Construct Curves over Finite Fields With Many Points
Gerard van der Geer, Marcel van der Vlugt
TL;DR
This paper presents various methods for constructing algebraic curves over finite fields that have a large number of rational points, supported by illustrative examples.
Contribution
It introduces new techniques for constructing such curves and demonstrates their effectiveness through concrete examples.
Findings
Methods successfully produce curves with many points
Examples validate the effectiveness of the methods
Potential applications in coding theory and cryptography
Abstract
In this paper we give several methods to construct curves over finite fields with many points and illustrate this with examples of the results.
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Taxonomy
TopicsCryptography and Residue Arithmetic