Some New Permutation Polynomials over Finite Fields

Nouara Zoubir; Kenza Guenda

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arXiv · 1705.01484

Some New Permutation Polynomials over Finite Fields

Nouara Zoubir·Kenza Guenda

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Abstract

In this paper, we construct a new class of complete permutation monomials and several classes of permutation polynomials. Further, by giving another characterization of o-polynomials, we obtain a class of permutation polynomials of the form $G(x)+ \gamma Tr(H(x))$, where G(X) is neither a permutation nor a linearized polynomial. This is an answer to the open problem 1 of Charpin and Kyureghyan in [P. Charpin and G. Kyureghyan, When does $G(x)+ \gamma Tr(H(x))$ permute $\mathbb{F}_{p^n}$?, Finite Fields and Their Applications 15 (2009) 615--632].

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Nouara Zoubir, Kenza Guenda. 2017-04-30. Some New Permutation Polynomials over Finite Fields. https://arxiv.org/abs/1705.01484

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