The maximum number of points on a curve of genus eight over the field of\n four elements

2020/04/16 by Everett W. Howe, Howe, Everett W. · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2004.08007

Abstract

The Oesterl 'e bound shows that a curve of genus 8 over the finite field\n mathbbF₄ can have at most 24 rational points, and Niederreiter and Xing\nused class field theory to show that there exists such a curve with 21 points.\nWe improve both of these results: We show that a genus-8 curve over\n mathbbF₄ can have at most 23 rational points, and we provide an example\nof such a curve with 22 points, namely the curve defined by the two equations\ny² + (x³ + x + 1)y = x⁶ + x⁵ + x⁴ + x² and z³ = (x+1)y + x².\n

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• Refinements on higher order Weil-Oesterlé bounds via a Serre type argument

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