Abstract
We study permutation polynomials of the shape F(X) = G(X) + γ Tr(H(X)) over \(\mathbb{F}_{2^n}\) . We prove that if the polynomial G(X) is a permutation polynomial or a linearized polynomial, then the considered problem can be reduced to finding Boolean functions with linear structures. Using this observation we describe six classes of such permutation polynomials.
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Charpin, P., Kyureghyan, G.M. (2008). On a Class of Permutation Polynomials over \(\mathbb{F}_{2^n}\) . In: Golomb, S.W., Parker, M.G., Pott, A., Winterhof, A. (eds) Sequences and Their Applications - SETA 2008. SETA 2008. Lecture Notes in Computer Science, vol 5203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85912-3_32
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DOI: https://doi.org/10.1007/978-3-540-85912-3_32
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