1. A new family of maximal curves.
- Author
-
Beelen, Peter and Montanucci, Maria
- Subjects
- *
AUTOMORPHISM groups , *GROUP theory , *MATHEMATICAL symmetry , *ELLIPTIC curves , *ALGEBRAIC curves , *NUMBER theory - Abstract
In this article we construct for any prime power q and odd n⩾5, a new Fq2n‐maximal curve Xn. Like the Garcia–Güneri–Stichtenoth maximal curves, our curves generalize the Giulietti–Korchmáros 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. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF