Classes of permutation polynomials based on cyclotomy and an additive analogue

TL;DR

This paper introduces new classes of permutation polynomials using cyclotomy and additive analogues, expanding on recent mathematical results and providing novel constructions with potential applications in finite field theory.

Contribution

It presents a generalized construction of permutation polynomials based on cyclotomy and additive analogues, including a novel approach with no multiplicative analogue.

Findings

New classes of permutation polynomials introduced

Generalization of recent mathematical results

Additive analogue construction with no multiplicative counterpart

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 J. Marcos from arXiv:0810.2738v1.