We investigate two families S~q and R~q of maximal curves over finite fields recently constructed by Skabelund as cyclic covers of the Suzuki and Ree curves. We show that S~q is not Galois covered by the Hermitian curve maximal over Fq4, and R~q is not Galois covered by the Hermitian curve maximal over Fq6. We also compute the genera of many Galois subcovers of S~q and R~q; in this way, many new values in the spectrum of genera of maximal curves are obtained. The full automorphism group of both S~q and R~q is determined

Giulietti, M., Montanucci, M., Quoos, L., Zini, G. (2018). On some Galois covers of the Suzuki and Ree curves. JOURNAL OF NUMBER THEORY, 189, 220-254 [10.1016/j.jnt.2017.12.005].

On some Galois covers of the Suzuki and Ree curves

Zini, G
2018

Abstract

We investigate two families S~q and R~q of maximal curves over finite fields recently constructed by Skabelund as cyclic covers of the Suzuki and Ree curves. We show that S~q is not Galois covered by the Hermitian curve maximal over Fq4, and R~q is not Galois covered by the Hermitian curve maximal over Fq6. We also compute the genera of many Galois subcovers of S~q and R~q; in this way, many new values in the spectrum of genera of maximal curves are obtained. The full automorphism group of both S~q and R~q is determined
Articolo in rivista - Articolo scientifico
Automorphism group; Deligne-Lusztig curves; Maximal curve; Algebra and Number Theory
English
2018
189
220
254
none
Giulietti, M., Montanucci, M., Quoos, L., Zini, G. (2018). On some Galois covers of the Suzuki and Ree curves. JOURNAL OF NUMBER THEORY, 189, 220-254 [10.1016/j.jnt.2017.12.005].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/189918
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