New Classes of Permutation Polynomials Having the Forms

A class of permutation polynomials of the form (x^2k + x + )^s + x was derived by Zeng-Zhu-Hu in 2010, and this was generalized to similar forms by Zha-Hu in 2012, by Tu-Zeng-Jiang and Tu-Zeng-Li-Helleseth in 2015, and by Zha-Hu in 2016. Using techniques inspired by the work of Zeng-Zhu-Hu, new classes of permutation polynomials of the forms (ax^pk -ax + ) ^s +x and  (ax^pj + bx^pk + cx + )^s + x are derived.

Keywords: finite fields, permutation polynomials

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 E-mail: suphawanj@nu.ac.th