Cyclotomy and permutation polynomials of large indices

TL;DR

This paper introduces a cyclotomy-based method to systematically generate new classes of permutation polynomials over finite fields, especially those with large indices, enhancing the toolkit for finite field applications.

Contribution

It presents an algorithmic approach to construct permutation polynomials using cyclotomy, expanding the known classes with a focus on large indices.

Findings

Generated numerous new permutation polynomial classes

Demonstrated the effectiveness of cyclotomy in polynomial construction

Provided explicit examples of permutation polynomials with large indices

Abstract

We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way. Many of them are permutation polynomials of large indices.