In this paper we introduce the notion of Dickson polynomials of the (k+1)-th kind over finite fields Fpm and study basic properties of this family of polynomials. In particular, we study the factorization and the permutation behavior of Dickson polynomials of the third kind.

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Keywords Dickson polynomials, Factorization, Finite fields, Permutation polynomials
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Journal Finite Fields and their Applications
Wang, Q, & Yucas, J.L. (Joseph L.). (2012). Dickson polynomials over finite fields. Finite Fields and their Applications, 18(4), 814–831. doi:10.1016/j.ffa.2012.02.001