In this note, we give a shorter proof of the result of Zheng, Yu, and Pei on the explicit formula of inverses of generalized cyclotomic permutation polynomials over finite fields. Moreover, we characterize all these cyclotomic permutation polynomials that are involutions. Our results provide a fast algorithm (only modular operations are involved) to generate many classes of generalized cyclotomic permutation polynomials, their inverses, and involutions.

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Keywords Cyclotomic mappings, Finite fields, Inverse polynomials, Involutions, Permutation polynomials
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Journal Finite Fields and their Applications
Wang, Q. (2017). A note on inverses of cyclotomic mapping permutation polynomials over finite fields. Finite Fields and their Applications, 45, 422–427. doi:10.1016/j.ffa.2017.01.006