On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields

2014-09-18
Özbudak, Ferruh
GÜLMEZ TEMÜR, BURCU
YAYLA, OĞUZ
We determined the number of rational points of fibre products of two Kummer covers over a rational point of the projective line in a recent work of F. Ozbudak and B. G. Temur (Des Codes Cryptogr 70(3): 385-404, 2014), where we also constructed explicit examples, including a record and two new entries for the current Table of Curves with Many Points (manYPoints: Table of curves with many points. http://www.manypoints.org (2014). Accessed 30 Sep 2014). Using the methods given in Ozbudak and Gulmez Temur (Des Codes Cryptogr 70(3): 385-404, 2014), we made an exhaustive computer search over F-5 and F-7 by the contributions of O. Yayla and at the end of this search we obtained 12 records and 6 new entries for the current table; in particular, we observed that the fibre product with genus 7 and 36 rational points coincides with the Ihara bound, thus we concluded that the maximum number N-7(7) of F-7-rational points among all curves of genus 7 is 36 (Ozbudak et al., Turkish J Math 37(6): 908-913, 2013). Recently, we made another exhaustive computer search over F-11. In this paper we are representing the results as three records and three new entries for the current table.
Citation Formats
F. Özbudak, B. GÜLMEZ TEMÜR, and O. YAYLA, “On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields,” 2014, vol. 3, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47954.