Constructing permutation polynomials using generalized Redei functions

2023/05/10 by Zhiguo Ding, Ding, Zhiguo, Michael E. Zieve +1
Computer Science · Engineering · #11T06 (Primary) #Cellular Automata and Applications #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2305.06322

openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine all permutations in two large classes of polynomials over finite fields, where the construction of the polynomials in each class involves the denominators of a class of rational functions generalizing the classical Redei functions. Our results generalize eight recent results from the literature, and our proofs of our more general results are much shorter and simpler than the previous proofs of special cases.

Related

• A Construction of Permutation Polynomials Using Rédei Function in Even Characteristic
• A Recursive Construction of Permutation Polynomials over \mathbbF_q² with Odd Characteristic from Rédei Functions
• Permutation polynomials over finite fields from low-degree rational functions
• Further Results on Permutation Polynomials over Finite Fields
• Specific permutation polynomials over finite fields