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A new family of maximal curves
- Source :
- Beelen, P & Montanucci, M 2018, ' A new family of maximal curves ', Journal of the London Mathematical Society, vol. 98, no. 2, pp. 573-592 . https://doi.org/10.1112/jlms.12144
- Publication Year :
- 2017
-
Abstract
- In this article we construct for any prime power q and odd n ≥ 5, a new Fq2n -maximal curve Xn. Like the Garcia–G¨uneri–Stichtenoth maximal curves, our curves generalize the Giulietti–Korchmaros maximal curve, though in a different way. We compute the full automorphism group of Xn, yielding that it has precisely q(q2 − 1)(qn + 1) automorphisms. Further, we show that unless q = 2, the curve Xn is not a Galois subcover of the Hermitian curve. Finally, up to our knowledge, we find new values of the genus spectrum of Fq2n -maximal curves, by considering some Galois subcovers of Xn.
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Beelen, P & Montanucci, M 2018, ' A new family of maximal curves ', Journal of the London Mathematical Society, vol. 98, no. 2, pp. 573-592 . https://doi.org/10.1112/jlms.12144
- Accession number :
- edsair.doi.dedup.....fe956ea79fb3261204b85fd965cb1aa4