Classes of Permutation Polynomials Based on Cyclotomy and an Additive Analogue

Abstract

I present a construction of permutation polynomials based on cyclotomy, an additive analogue of this construction, and a generalization of this additive analogue which appears to have no multiplicative analogue. These constructions generalize recent results of José Marcos. Dedicated to Mel Nathanson on the occasion of his sixtieth birthday

Further results on permutation polynomials over finite fields

“…Recently, Akbary, Ghioca and Wang derived a lemma about permutations on finite sets [1], which contains Lemma 2.1 in [29] and Proposition 3 in [31] as special cases, and employed this lemma to unify some earlier constructions and developed new constructions of permutation polynomials over finite fields. In [25], with this lemma we derived several theorems about permutation polynomials over finite fields.…”

Constructing permutations of finite fields via linear translators

“…⋄ Remark 1 A particular case of Corollary 1 and Theorem 4 for b = 0 are proved in [8] for permutations x + h(T r(x)), where h : F q → F q and q is a prime number. In [8] and [11] further permutations of F q n involving additive mappings are constructed.…”

Permutation polynomials over finite fields — A survey of recent advances

“…In each case, a commutative diagram is included to indicate the unified AGW approach which may be different from the original proof of the result. The following fact is frequently used to illustrate the commutativity of a diagram: Let [92].) Let g ∈ F q [X] and A, h ∈ F p [X], where p = char F q and A is p-linearized.…”