Browsing by Author "Temur, Burcu Gulmez"
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Article Citation Count: 7Classification of permutation polynomials of the form x3g(xq-1) of Fq2 where g(x) = x3 + bx plus c and b, c ∈ Fq*(Springer, 2022) Gülmez Temür, Burcu; Temur, Burcu Gulmez; MathematicsWe 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.Article Citation Count: 3Classification of some quadrinomials over finite fields of odd characteristic(Academic Press inc Elsevier Science, 2023) Gülmez Temür, Burcu; Temur, Burcu Gulmez; MathematicsIn this paper, we completely determine all necessary and sufficient conditions such that the polynomial f(x) = x3 + axq +2 + bx2q +1 + cx3q, where a, b, c is an element of Fq*, is a permutation quadrinomial of Fq2 over any finite field of odd characteristic. This quadrinomial has been studied first in [25] by Tu, Zeng and Helleseth, later in [24] Tu, Liu and Zeng revisited these quadrinomials and they proposed a more comprehensive characterization of the coefficients that results with new permutation quadrinomials, where char(Fq) = 2 and finally, in [16], Li, Qu, Li and Chen proved that the sufficient condition given in [24] is also necessary and thus completed the solution in even characteristic case. In [6] Gupta studied the permutation properties of the polynomial x3 + axq +2 + bx2q +1 + cx3q, where char(Fq) = 3, 5 and a, b, c is an element of Fq* and proposed some new classes of permutation quadrinomials of Fq2 . In particular, in this paper we classify all permutation polynomials of Fq2 of the form f(x) = x3 + axq +2 + bx2q +1 + cx3q, where a, b, c is an element of Fq*, over all finite fields of odd characteristic and obtain several new classes of such permutation quadrinomials. (c) 2022 Elsevier Inc. All rights reserved.Article Citation Count: 2Complete characterization of some permutation polynomials of the form xr(1+axs1(q-1)+bxs2(q-1)) over Fq2(Springer, 2023) Gülmez Temür, Burcu; Temur, Burcu Gulmez; MathematicsWe completely characterize all permutation trinomials of the form f (x) = x(3)(1 + ax(q-1) + bx(2(q-1))) over F-q2, where a, b is an element of F-q* and all permutation trinomials of the form f (x) = x(3)(1 + bx(2(q-1)) + cx(3(q-1))) over F-q2, where b, c is an element of F-q* in both even and odd characteristic cases.Article Citation Count: 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) Gülmez Temür, Burcu; Temur, Burcu Gulmez; Yayla, Oguz; MathematicsIn 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 Count: 5Finite number of fibre products of Kummer covers and curves with many points over finite fields(Springer, 2014) Gülmez Temür, Burcu; Temur, Burcu Gulmez; MathematicsWe 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 Count: 1FURTHER RESULTS ON FIBRE PRODUCTS OF KUMMER COVERS AND CURVES WITH MANY POINTS OVER FINITE FIELDS(Amer inst Mathematical Sciences-aims, 2016) Gülmez Temür, Burcu; Temur, Burcu Gulmez; Yayla, Oguz; MathematicsWe 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).Article Citation Count: 0On a class of permutation trinomials over finite fields(Tubitak Scientific & Technological Research Council Turkey, 2024) Gülmez Temür, Burcu; Ozkaya, Buket; MathematicsIn this paper, we study the permutation properties of the class of trinomials of the form f (x ) = x( 4q+1 )+ lambda (1 )x (q +4) + lambda( 2 )x (2q +3) is an element of F (q) 2 [x ] , where lambda( 1 ), lambda (2) is an element of F (q) and they are not simultaneously zero. We find all necessary and sufficient conditions on lambda (1) and lambda (2) such that f (x ) permutes F( q )2 , where q is odd and q = 2( 2k+1) , k is an element of N.Conference Object Citation Count: 0On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields(Springer-verlag Berlin, 2015) Gülmez Temür, Burcu; Temur, Burcu Gulmez; Yayla, Oguz; MathematicsWe 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.Article Citation Count: 1A short note on permutation trinomials of prescribed type(Taylor & Francis inc, 2020) Akbal, Yıldırım; Temur, Burcu Gulmez; Gülmez Temür, Burcu; MathematicsWe show that there are no permutation trinomials of the form hox 1/4 x5 ox5oq1 xq1 1 over Fq2 where q is not a power of 2. Together with a result of Zha, Z., Hu, L., Fan, S., hox permutes Fq2 if q 1/4 2k where k 2 omod 4, this gives a complete classification of those q's such that hox permutes F-q(2).Article Citation Count: 3A specific type of permutation and complete permutation polynomials over finite fields(World Scientific Publ Co Pte Ltd, 2020) Gülmez Temür, Burcu; Temur, Burcu Gulmez; 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.