Algebraic Structure of Permutational Polynomials over \mathbbF_qⁿ \uppercase\expandafter\romannumeral2

2025/03/28 by Pingzhi Yuan, Yuan, Pingzhi, Xuan Pang +3
Computer Science · #11T06 #11T55 #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2503.22415

openalex publication_date 2025/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that there exists a significant equivalence between the vector space \mathbbF_qⁿ and the finite fields \mathbbF_qⁿ, and many scholars often view them as the same in most contexts. However, the precise connections between them still remain mysterious. In this paper, we first show their connections from an algebraic perspective, and then propose a more general algebraic framework theorem. Furthermore, as an application of this generalized algebraic structure, we give some classes of permutation polynomials over \mathbbF_q².

Related

• Algebraic Structure of Permutational Polynomials over \mathbbF_qⁿ
• Permutation Polynomials of \mathbbF_q² : A Linear Algebraic Approach
• Further results on some classes of permutation polynomials over finite fields
• Further Results on Permutation Polynomials over Finite Fields
• Five Constructions of Permutation Polynomials over \gf(q²)