Permutation polynomials over finite fields by the local criterion

2024/09/27 by Danyao Wu, Pingzhi Yuan, Wu, Danyao +1
Computer Science · Engineering · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2409.18758

openalex publication_date 2024/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we further investigate the local criterion and present a class of permutation polynomials and their compositional inverses over \mathbbF_q². Additionally, we demonstrate that linearized polynomial over \mathbbF_qⁿ is a local permutation polynomial with respect to all linear transformations from \mathbbF_qⁿ to \mathbbF_q , and that every permutation polynomial is a local permutation polynomial with respect to certain mappings.

Related

• The compositional inverses of three classes of permutation polynomials over finite fields
• Permutation Polynomials of \mathbbF_q² : A Linear Algebraic Approach
• The compositional inverses of three classes of permutation polynomials over finite fields
• Permutation and local permutation polynomial of maximum degree
• Permutation polynomials from a linearized decomposition