Permutation Polynomials of Degree 6 or 7 over Finite Fields of Characteristic 2

2010/02/14 by Jiyou Li, Li, Jiyou, David B. Chandler +3 · 2 citations
Computer Science · #11T06 #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1002.2796

openalex publication_date 2010/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In \citeD1, Dickson listed all permutation polynomials up to degree 5 over an arbitrary finite field, and all permutation polynomials of degree 6 over finite fields of odd characteristic. The classification of degree 6 permutation polynomials over finite fields of characteristic 2 was left incomplete. In this paper we complete the classification of permutation polynomials of degree 6 over finite fields of characteristic 2. In addition, all permutation polynomials of degree 7 over finite fields of characteristic 2 are classified.

Cited by

• Determination of Some Types of Permutations over \mathbbF_q² with Low-Degree
• Orthomorphism Polynomials of degree 7 over finite fields

Related

• A note on two classes of permutation polynomials over finite fields
• Specific permutation polynomials over finite fields
• Further results on some classes of permutation polynomials over finite fields
• Some New Permutation Polynomials over Finite Fields
• Orthomorphism Polynomials of degree 7 over finite fields