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arXiv · 1910.11098

New examples of maximal curves with low genus

Daniele Bartoli·Massimo Giulietti·Mokoto Kawakita·Maria Montanucci
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Abstract

We investigate the Jacobian decomposition of some algebraic curves over finite fields with genus $4$, $5$ and $10$. As a corollary, explicit equations for curves that are either maximal or minimal over the finite field with $p^2$ elements are obtained for infinitely many $p$'s. Lists of small $p$'s for which maximality holds are provided. In some cases we describe the automorphism group of the curve.

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Daniele Bartoli, Massimo Giulietti, Mokoto Kawakita, Maria Montanucci. 2019-12-09. New examples of maximal curves with low genus. https://arxiv.org/abs/1910.11098

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