Abstract
Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. In this paper, for an integer s satisfying \(s=\frac{q^n-1}{2}+q^r\), we give six classes of permutation polynomials of the form \((ax^{q^m}-bx+\delta )^s+L(x)\) over \(\mathbb {F}_{q^n}\), and for s satisfying \(s(p^m-1)\equiv p^m-1\ (mod\ p^n-1)\) or \(s(p^{{\frac{k}{2}}m}-1)\equiv p^{km}-1 (mod\ p^n-1)\), we propose three classes of permutation polynomials of the form \((aTr_m^n(x)+\delta )^s+L(x)\) over \(\mathbb {F}_{p^n}\), respectively.
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The authors are grateful to the anonymous reviewers for their careful reading of the original version of this paper, their detailed comments and suggestions, which have much improved the quality of this paper.
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This work is supported by the National Natural Science Foundation of China under Grant 61672414, the National Cryptography Development Fund under Grant MMJJ20170113, and the 111 Project under Grant B08038.
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Liu, Q., Sun, Y. & Zhang, W. Some classes of permutation polynomials over finite fields with odd characteristic. AAECC 29, 409–431 (2018). https://doi.org/10.1007/s00200-018-0350-6
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DOI: https://doi.org/10.1007/s00200-018-0350-6