Full classification of permutation rational functions and complete rational functions of degree three over finite fields
作者： Andrea Ferraguti , Giacomo Micheli
DOI: 10.1007/S10623-020-00715-0
关键词: Field (mathematics) 、 Mathematics 、 Prime power 、 Order (ring theory) 、 Polynomial (hyperelastic model) 、 Number theory 、 Degree (graph theory) 、 Combinatorics 、 Finite field 、 Rational function
摘要: Let q be a prime power, $$\mathbb {F}_q$$ the finite field of order and {F}_q(x)$$ rational functions over {F}_q$$. In this paper we classify count all $$\varphi \in \mathbb degree 3 that induce permutation {P}^1(\mathbb {F}_q)$$. As consequence our classification, can show there is no complete function unless $$3\mid q$$ $$ polynomial.
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