Abstract
Let Fq2 be the finite field with q2 elements. Most of the known Fq2 -maximal curves arise as quotient curves of the Fq2 -maximal Hermitian curve Hq. After a seminal paper by Garcia, Stichtenoth and Xing, many papers have provided genera of quotients of Hq, but their complete determination is a challenging open problem. In this paper we determine completely the spectrum of genera of quotients of Hq for any q ≡ 1 (mod 4).
Original language | English |
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Journal | Journal of Algebra |
Volume | 550 |
Pages (from-to) | 23-53 |
ISSN | 0021-8693 |
DOIs | |
Publication status | Published - 2020 |
Keywords
- Hermitian curve
- Unitary groups
- Quotient curves
- Maximal curves