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arXiv · 0707.1110

On some permutation polynomials over F_q of the form x^r*h(x^((q-1)/d)))

Michael E. Zieve
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Abstract

In a recent paper, Akbary and Wang gave a sufficient condition for x^u + x^r to permute GF(q), in terms of the period of a certain sequence involving sums of cosines. As an application they gave necessary and sufficient conditions in case u,r,q satisfy certain special properties. We show that the Akbary-Wang sufficient condition follows from a more general sufficient condition which does not involve sums of cosines. This leads to vastly simpler proofs of the Akbary-Wang results, as well as generalizations to polynomials of the form x^r*h(x^{(q-1)/d}).

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Michael E. Zieve. 2007-07-07. On some permutation polynomials over F_q of the form x^r*h(x^((q-1)/d))). https://arxiv.org/abs/0707.1110

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