We investigate two families Sq and Rq of maximal curves over finite fields recently constructed by Skabelund as cyclic covers of the Suzuki and Ree curves. We show that Sq is not Galois covered by the Hermitian curve maximal over $F_q^4$, and Rq is not Galois covered by the Hermitian curve maximal over $F_q^6$. We also compute the genera of many Galois subcovers of Sq and Rq; in this way, many new values in the spectrum of genera of maximal curves are obtained. The full automorphism group of both Sq and Rq is determined.
On some Galois covers of the Suzuki and Ree curves
Giulietti, M.;Montanucci, M.;Zini, G.
2018
Abstract
We investigate two families Sq and Rq of maximal curves over finite fields recently constructed by Skabelund as cyclic covers of the Suzuki and Ree curves. We show that Sq is not Galois covered by the Hermitian curve maximal over $F_q^4$, and Rq is not Galois covered by the Hermitian curve maximal over $F_q^6$. We also compute the genera of many Galois subcovers of Sq and Rq; in this way, many new values in the spectrum of genera of maximal curves are obtained. The full automorphism group of both Sq and Rq is determined.File in questo prodotto:
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