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      On the Tu-Zeng Permutation Trinomial of Type \((1/4,3/4)\)

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          Abstract

          Let \(q\) be a power of \(2\). Recently, Tu and Zeng considered trinomials of the form \(f(X)=X+aX^{(1/4)q^2(q-1)}+bX^{(3/4)q^2(q-1)}\), where \(a,b\in\Bbb F_{q^2}^*\). They proved that \(f\) is a permutation polynomial of \(\Bbb F_{q^2}\) if \(b=a^{2-q}\) and \(X^3+X+a^{-1-q}\) has no root in \(\Bbb F_q\). In this paper, we show that the above sufficient condition is also necessary.

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          Most cited references 6

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          Permutation polynomials and group permutation polynomials

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            Determination of a type of permutation trinomials over finite fields, II

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              On a conjecture about a class of permutation trinomials

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                Author and article information

                Journal
                17 June 2019
                Article
                1906.07240

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                11T06, 11T55, 14H05
                24 pages
                math.NT

                Number theory

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