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
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
