# Permutations via linear translators

Abstract : We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first characterize some functions having linear translators, based on which several families of permutations are then derived. Extending the results of \cite{kyu}, we give in several cases the compositional inverse of these permutations. The connection with complete permutations is also utilized to provide further infinite classes of permutations. Moreover, we propose new tools to study permutations of the form $x\mapsto x+(x^{p^m}-x+\delta)^s$ and a few infinite classes of permutations of this form are proposed.
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Cited literature [19 references]

https://hal.inria.fr/hal-01412487
Contributor : Pascale Charpin <>
Submitted on : Monday, December 12, 2016 - 2:21:05 PM
Last modification on : Thursday, April 26, 2018 - 10:28:07 AM
Long-term archiving on: Monday, March 27, 2017 - 7:26:59 PM

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### Citation

Nastja Cepak, Pascale Charpin, Enes Pasalic. Permutations via linear translators. Finite Fields and Their Applications, Elsevier, 2017, 45, pp.19--42. ⟨10.1016/j.ffa.2016.11.009⟩. ⟨hal-01412487v2⟩

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