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On the spectrum for the genera of maximal curves over small fields

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  • Motivated by previous computations in Garcia, Stichtenoth and Xing (2000) paper [11], we discuss the spectrum $\mathbf{M}(q^2)$ for the genera of maximal curves over finite fields of order $q^2$ with $7≤ q≤ 16$. In particular, by using a result in Kudo and Harashita (2016) paper [22], the set $\mathbf{M}(7^2)$ is completely determined.

    Mathematics Subject Classification: Primary: 11G20, 11M38, 14H05, 14G15; Secondary: 14HXX.


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