For each prime power ℓ the plane curve Xℓ with equation Yℓ2ℓ+1=Xℓ2-X is maximal over Fℓ6. Garcia and Stichtenoth in 2006 proved that X3 is not Galois covered by the Hermitian curve and raised the same question for Xℓ with ℓ>3; in this paper we show that Xℓ is not Galois covered by the Hermitian curve for any ℓ>3. Analogously, Duursma and Mak proved that the generalized GK curve Cℓn over Fℓ2n is not a quotient of the Hermitian curve for ℓ>2 and n≥5, leaving the case ℓ=2 open; here we show that C2n is not Galois covered by the Hermitian curve over F22n for n≥5.

On maximal curves that are not quotients of the Hermitian curve / Giulietti, M.; Montanucci, M.; Zini, G.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 41:(2016), pp. 72-88. [10.1016/j.ffa.2016.05.005]

On maximal curves that are not quotients of the Hermitian curve

Zini G.
2016

Abstract

For each prime power ℓ the plane curve Xℓ with equation Yℓ2ℓ+1=Xℓ2-X is maximal over Fℓ6. Garcia and Stichtenoth in 2006 proved that X3 is not Galois covered by the Hermitian curve and raised the same question for Xℓ with ℓ>3; in this paper we show that Xℓ is not Galois covered by the Hermitian curve for any ℓ>3. Analogously, Duursma and Mak proved that the generalized GK curve Cℓn over Fℓ2n is not a quotient of the Hermitian curve for ℓ>2 and n≥5, leaving the case ℓ=2 open; here we show that C2n is not Galois covered by the Hermitian curve over F22n for n≥5.
2016
41
72
88
On maximal curves that are not quotients of the Hermitian curve / Giulietti, M.; Montanucci, M.; Zini, G.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 41:(2016), pp. 72-88. [10.1016/j.ffa.2016.05.005]
Giulietti, M.; Montanucci, M.; Zini, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1258119
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