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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 GulmezWe 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: 12Citation - Scopus: 13Classification of Some Quadrinomials Over Finite Fields of Odd Characteristic(Academic Press inc Elsevier Science, 2023) Ozbudak, Ferruh; Temur, Burcu GulmezIn 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 - WoS: 2Citation - Scopus: 2Further 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, OguzWe 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 - WoS: 7Citation - Scopus: 10Complete Characterization of Some Permutation Polynomials of the Form Xr(1+axs1(q-1)< Over Fq2(Springer, 2023) Ozbudak, Ferruh; Temur, Burcu GulmezWe 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 - WoS: 13Citation - Scopus: 12Classification 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 GulmezWe 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.
