Reciprocal polynomials and curves with many points over a finite field

2021/10/20 by Rohit Gupta, Gupta, Rohit, Erik A. R. Mendoza +3
Computer Science · Mathematics · #11G20 #14G05 #14G15 #14H05 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.10620

openalex publication_date 2021/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbb F_q² be the finite field with q² elements. We provide a simple and effective method, using reciprocal polynomials, for the construction of algebraic curves over \mathbb F_q² with many rational points. The curves constructed are Kummer covers or fibre products of Kummer covers of the projective line. Further, we compute the exact number of rational points for some of the curves.

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