2022/07/27 by Hutao Song, Hua Guo, Song, Hutao +7
Computer Science · Engineering · Social Sciences · #Advanced Wireless Communication Techniques #Coding theory and cryptography #FOS: Mathematics #Islamic Finance and Communication #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2207.13335
openalex publication_date 2022/07/27 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
Permutation polynomials with coefficients 1 over finite fields attract researchers' interests due to their simple algebraic form. In this paper, we first construct four classes of fractional permutation polynomials over the cyclic subgroup of \mathbbF22m . From these permutation polynomials, three new classes of permutation polynomials with coefficients 1 over \mathbbF22m are constructed, and three more general new classes of permutation polynomials with coefficients 1 over \mathbbF22m are constructed using a new method we presented recently. Some known permutation polynomials are the special cases of our new permutation polynomials. Furthermore, we prove that, in all new permutation polynomials, there exists a permutation polynomial which is EA-inequivalent to known permutation polynomials for all even positive integer m . This proof shows that EA-inequivalent permutation polynomials over \mathbbFq can be constructed from EA-equivalent permutation polynomials over the cyclic subgroup of \mathbbFq . From this proof, it is obvious that, in all new permutation polynomials, there exists a permutation polynomial of which algebraic degree is the maximum algebraic degree of permutation polynomials over \mathbbF22m .