Report
Enumerating hyperelliptic curves over finite fields in quasilinear time
| العنوان: | Enumerating hyperelliptic curves over finite fields in quasilinear time |
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| المؤلفون: | Howe, Everett W. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11G20 (Primary) 11Y16, 14G15, 14H10, 14H25 (Secondary) |
| الوصف: | We present an algorithm that, for every fixed genus $g$, will enumerate all hyperelliptic curves of genus $g$ over a finite field $k$ of odd characteristic in quasilinear time; that is, the time required for the algorithm is $\widetilde{O}(q^{2g-1})$, where $q=\#k$. Such an algorithm already exists in the case $g=2$, thanks to work of Mestre and Cardona and Quer, and in the case $g=3$, thanks to work of Lercier and Ritzenthaler. Experimentally, it appears that our new algorithm is about two orders of magnitude faster in practice than ones based on their work. Comment: 23 pages. Corrected small typos, added a reference to a paper of Nart, and added links to Internet Archive library copies of two books |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.15255 |
| رقم الانضمام: | edsarx.2401.15255 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |