Classification of permutation polynomials of the form <i>x</i><SUP>3</SUP><i>g</i>(<i>x</i><SUP><i>q</i>-1</SUP>) of F<sub><i>q</i>2</sub> where <i>g</i>(<i>x</i>) = <i>x</i><SUP>3</SUP> + <i>bx</i> plus <i>c</i> and <i>b</i>, <i>c</i> ∈ F<i><sub>q</sub></i>*

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Date

2022

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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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Abstract

We 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.

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Ozbudak, Ferruh/0000-0002-1694-9283

Keywords

Finite fields, Permutation polynomials, Absolutely irreducible

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Citation

7

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Q2

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Volume

90

Issue

7

Start Page

1537

End Page

1556

URI

https://doi.org/10.1007/s10623-022-01052-0
 https://hdl.handle.net/20.500.14411/1753

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