Browsing by Author "Yayla, Oguz"

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Citation - WoS: 1
An exhaustive computer search for finding new curves with many points among fibre products of two Kummer covers over F₅ and F₇
(Tubitak Scientific & Technological Research Council Turkey, 2013) Ozbudak, Ferruh; Temur, Burcu Gulmez; Yayla, Oguz; Mathematics
In this paper we make an exhaustive computer search for finding new curves with many points among fibre products of 2 Kummer covers of the projective line over F-5 and F-7. At the end of the search, we have 12 records and 6 new entries for the current Table of Curves with Many Points. In particular, we observe that the fibre product y(1)(3)= 5(x + 2)(x + 5)/x, y(2)(3)= 3x(2()x + 5)/x + 3 over F-7 has genus 7 with 36 rational points. As this coincides with the Ihara bound, we conclude that the maximum number N-7(7) of F-7-rational points among all curves of genus 7 is 36. Our exhaustive search has been possible because of the methods given in the recent work by Ozbudak and Temur (2012) for determining the number of rational points of such curves.
Citation - WoS: 1
Citation - Scopus: 1
Further Results on Fibre Products of Kummer Covers and Curves With Many Points Over Finite Fields
(Amer inst Mathematical Sciences-aims, 2016) Ozbudak, Ferruh; Temur, Burcu Gulmez; Yayla, Oguz; Mathematics
We study fibre products of an arbitrary number of Kummer covers of the projective line over F-q under suitable weak assumptions. If q - 1 = r(n) for some prime r, then we completely determine the number of rational points over a rational point of the projective line. Using this result we obtain explicit examples of fibre products of three Kummer covers supplying new entries for the current table of curves with many points (http://www.manypoints.org,October 31 2015).
Citation - WoS: 1
Citation - Scopus: 1
The Number of Irreducible Polynomials Over Finite Fields With Vanishing Trace and Reciprocal Trace
(Springer, 2022) Cakiroglu, Yagmur; Yayla, Oguz; Yilmaz, Emrah Sercan; Mathematics
We present the formula for the number of monic irreducible polynomials of degree n over the finite field F-q where the coefficients of x(n)(-1) and x vanish for n >= 3. In particular, we give a relation between rational points of algebraic curves over finite fields and the number of elements a is an element of F-qn for which Trace(a) = 0 and Trace(a(-1)) = 0.
On Fibre Products of Kummer Curves With Many Rational Points Over Finite Fields
(Springer-verlag Berlin, 2015) Ozbudak, Ferruh; Temur, Burcu Gulmez; Yayla, Oguz; Mathematics
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.