Quotient curves of the GK curve

Fanali, Stefania; Giulietti, Massimo

doi:10.1515/advgeom.2011.046

Cited by 18 publications

(14 citation statements)

References 28 publications

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“…The results of Sections 7 and 8 provide many new genera for F q 4 -maximal curves in characteristic 2 and for F q 6 -maximal curves in characteristic 3. To exemplify this fact, Table 1 shows genera of F 8 4 -, F 8 5 -, and F 27 6 -maximal curves which are new, up to our knowledge; that is, they are new with respect to the genera provided by [1,2,3,5,6,7,8,10,12,13].…”

Section: = H × C N Withh Centralizing An Involution ι ∈ R(q)mentioning

confidence: 99%

On some Galois covers of the Suzuki and Ree curves

Giulietti¹,

Montanucci²,

Quoos³

et al. 2018

Journal of Number Theory

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We determine the full automorphism group of two recently constructed families S q andR q of maximal curves over finite fields. These curves are cyclic covers of the Suzuki and Ree curves, and are analogous to the Giulietti-Korchmáros cover of the Hermitian curve. We show thatS q is not Galois covered by the Hermitian curve maximal over F q 4 , andR q is not Galois covered by the Hermitian curve maximal over F q 6 . Finally, we compute the genera of many Galois subcovers ofS q andR q ; this provides new genera for maximal curves.Lemma 13. The lifted group LR(q) contains a subgroupR(q) isomorphic to the Ree group Aut(R q ).Lemma 14. The normalizer of C m in Aut(R q ) is the direct productR(q) × C m .Corollary 15. The group LR(q) coincides with the normalizer of C m in Aut(R q ).

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Section: = H × C N Withh Centralizing An Involution ι ∈ R(q)mentioning

confidence: 99%

On some Galois covers of the Suzuki and Ree curves

Giulietti¹,

Montanucci²,

Quoos³

et al. 2018

Journal of Number Theory

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“…For several of these, no maximal function field of this genus was previously known to the best of our knowledge. We compared our results with the genera of maximal function fields given in [1,2,3,4,6,8,12]. Some of the new genera for small values of n and q are as follows.…”

Section: Now We Can Calculate the Expressions Appearing In Equationmentioning

confidence: 99%

A complete characterization of Galois subfields of the generalized Giulietti–Korchmáros function field

Anbar¹,

Bassa

Beelen³

2017

Finite Fields and Their Applications

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“…By Theorem 3.12 and Theorem 3.17, we can construct the maximal function fields over the finite fields of the cardinalities 5 6 , 5 10 , 3 10 and 3 18 with the following genera which are new up to [2], [4], [6], [8]: …”

Section: Examplementioning

confidence: 99%

“…Some subfields of the GK function field are described in [4], and some new genera are obtained by a strong group-theoretic arguments. Here, we construct some subgroups of GK and generalized GK function field with similar techniques that were used in [2,6], and we get some new genera as well as many of the genera that were obtained in [4].…”

Section: Introductionmentioning

confidence: 99%