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Article Citation - WoS: 3Citation - Scopus: 4Some Permutations and Complete Permutation Polynomials Over Finite Fields(Tubitak Scientific & Technological Research Council Turkey, 2019) Ongan, Pınar; Temür, Burcu GülmezIn this paper we determine $b\\in F_{q^n}^\\ast$ for which the polynomial $f(x)=x^{s+1}+bx\\in F_{q^n}\\left[x\\right]$ is a permutationpolynomial and determine $b\\in F_{q^n}^\\ast$ for which the polynominal $f(x)=x^{s+1}+bx\\in F_{q^n}\\left[x\\right]$ is a complete permutationpolynomial where $s=\\frac{q^n-1}t,\\;t\\in\\mathbb{Z}^+$ such that $\\left.t\\;\\right|\\;q^n-1$.Master Thesis Sonlu Cisimler Üzerinde Permutasyon Polinomları(2017) Asad, Maha M.m. Dabboor; Temür, Burcu GülmezBu tezde sonlu cisimlerdeki permutasyon polinomları uzerine c¸alıs¸tık. Sonlu cisimler ¨ uzerinde tanımlanmıs¸ bazı permutasyon polinom tiplerinin olus¸turulması ve sınıflandı- ¨ rılması ile ilgili son zamanlarda yapılmıs¸ birtakım aras¸tırma sonuc¸larını derledik.Article An Exhaustive Computer Search for Finding New Curves With Many Points Among Fibre Products of Two Kummer Covers Over $\\bbb{f}_5$ and $\\bbb{f}_7$(2013) Özbudak, Ferruh; Temür, Burcu Gülmez; Yayla, OğuzIn 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 F5 and F7 . 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 $y^3_1$ = $\\frac {5(x+2)(x +5)} {x}$, $y^3_2$ $\\frac {3x^2(x +5)} {x + 3}$ over F7 has genus 7 with 36 rational points. As this coincides with the Ihara bound, we conclude that the maximum number N7 (7) of F7 -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 Özbudak and Temür (2012) for determining the number of rational points of such curves.
