Complete permutation polynomials induced from complete permutations of subfields

TL;DR

This paper introduces methods to construct complete permutation polynomials over finite fields using complete permutations of subfields, generalizing recent research and enabling new constructions in finite field theory.

Contribution

It presents novel techniques for deriving complete permutation polynomials from subfield permutations, expanding the toolkit for finite field constructions.

Findings

New techniques for constructing complete permutation polynomials

Generalization of recent results in finite field permutations

Applicable to extension fields via subfield permutations

Abstract

We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to construct complete permutations of certain extension fields with these techniques. The results generalize some recent work of several authors.