Complete Characterization of Some Permutation Polynomials of the Form X<sup>r</Sup>(1+ax<sup>s1(q-1)< Over F<sub>q2</Sub>

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Burcu_Gulmez_Temur_Complete characterization of some permutation polynomials.pdf (410.98 KB)

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2023

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Springer

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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We 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.

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Permutation Polynomials, Finite Fields, Absolutely Irreducible

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15

Issue

4

Start Page

775

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793

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https://doi.org/10.1007/s12095-023-00641-7
 https://hdl.handle.net/20.500.14411/2532

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