Permutation polynomials with Carlitz rank 2
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Let $\mathbb{F}_q$ denote the finite field with $q$ elements. The Carlitz rank of a permutation polynomial is a important measure of complexity of the polynomial. In this paper we find the sharp lower bound for the weight of any permutation polynomial with Carlitz rank $2$, improving the bound found by Gómez-Pérez, Ostafe and Topuzoğlu in that case.
10 pages, comments are welcome
Mathematics - Number Theory, Structure theory for finite fields and commutative rings (number-theoretic aspects), permutation polynomial, Polynomials over finite fields, FOS: Mathematics, Number Theory (math.NT), 12E20 (primary) and 11T30(secondary), Hermite criteria, Carlitz rank
Mathematics - Number Theory, Structure theory for finite fields and commutative rings (number-theoretic aspects), permutation polynomial, Polynomials over finite fields, FOS: Mathematics, Number Theory (math.NT), 12E20 (primary) and 11T30(secondary), Hermite criteria, Carlitz rank
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