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Article Citation - WoS: 6Citation - Scopus: 5Finite Number of Fibre Products of Kummer Covers and Curves With Many Points Over Finite Fields(Springer, 2014) Ozbudak, Ferruh; Temur, Burcu Gulmez; Gülmez Temür, BurcuWe study fibre products of a finite number of Kummer covers of the projective line over finite fields. We determine the number of rational points of the fibre product over a rational point of the projective line, which improves the results of Ozbudak and Temur (Appl Algebra Eng Commun Comput 18:433-443, 2007) substantially. We also construct explicit examples of fibre products of Kummer covers with many rational points, including a record and two new entries for the current table (http://www.manypoints.org, 2011).Article Citation - WoS: 1An 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; Gülmez Temür, BurcuIn 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.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 Gülmez; Gülmez Temür, BurcuIn 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 $\\left.t\\;\\right|\\;q^n-1$.Article Citation - WoS: 2A Specific Type of Permutation and Complete Permutation Polynomials Over Finite Fields(World Scientific Publ Co Pte Ltd, 2020) Ongan, Pinar; Gülmez Temür, Burcu; Temur, Burcu Gulmez; Gülmez Temür, Burcu; Mathematics; MathematicsIn this paper, we study polynomials of the form f(x) = x (qn-1/q-1+1) + bx is an element of F-qn[x], where n = 5 and list all permutation polynomials (PPs) and complete permutation polynomials (CPPs) of this form. This type of polynomials were studied by Bassalygo and Zinoviev for the cases n = 2 and n = 3, Wu, Li, Helleseth and Zhang for the case n = 4, p not equal 2, Bassalygo and Zinoviev answered the question for the case n = 4, p= 2 and finally by Bartoli et al. for the case n = 6. Here, we determine all PPs and CPPs for the case n = 5.Article Citation - WoS: 13Citation - Scopus: 13Classification of Permutation Polynomials of the Form x3< of Fq2< Where g(x< = x3< + bx Plus c and b, c ∈ Fq<(Springer, 2022) Ozbudak, Ferruh; Temur, Burcu Gulmez; Gülmez Temür, BurcuWe classify all permutation polynomials of the form x(3) g(x(q-1)) of F-q2 where g(x) = x(3) + bx + c and b, c is an element of F-q*. Moreover we find new examples of permutation polynomials and we correct some contradictory statements in the recent literature. We assume that gcd(3, q -1) = 1 and we use a well known criterion due to Wan and Lidl, Park and Lee, Akbary and Wang, Wang, and Zieve.
