2025/12/26 by Xuan Pang, Pang, Xuan, Danyao Wu +3
Computer Science · Engineering · #11T06 #11T55 #Advanced Wireless Communication Techniques #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems
paper · doi:10.48550/arxiv.2512.21908
openalex publication_date 2025/12/26 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28
Permutation polynomials over finite fields have extensive applications in various areas. Particularly, permutation polynomials with simple forms are of great interest. In recent papers, several classes of permutation polynomials of the form L(X)+Trqq3(h(X)) have been constructed. This paper further investigates permutation polynomials of such form over \mathbbFq3. Unlike previous studies, we transform the problem of constructing univariate permutation polynomials over finite fields into that of constructing corresponding multivariate permutations over \mathbbFq-vector spaces. Through this approach, we completely characterize a class of permutation polynomials of the form L(X)+γTrqq3(c1X+c2X2+c3X3+c4Xq+2) over \mathbbFq3, where q=2m, L(X)=Xq+aX and a,c1,c2,c3,c4,γ∈\mathbbFq with a2+a+1≠0. Furthermore, using a similar method, we generalize several results from a recent work by Jiang, Li and Qu (2026).