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Permutation polynomials of the form \((x^{p^m} - x + \delta)^s + L(x)\) over the finite field \(\mathbb{F}_{p^{2 m}}\) of odd characteristic. (English) Zbl 1315.05008
Summary: In this paper, we propose several classes of permutation polynomials with the form \((x^{p^m} - x + \delta)^s + L(x)\) over the finite field \(\mathbb{F}_{p^{2 m}}\), where \(p\) is an odd prime, and \(L(x)\) is a linearized polynomial with coefficients in \(\mathbb{F}_p\). The main method used in this paper is to determine the number of solutions of some equations over finite fields of odd characteristic.

MSC:
11T06 Polynomials over finite fields
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[1] Helleseth, T.; Zinoviev, V., New Kloosterman sums identities over \(\mathbb{F}_{2^m}\) for all m, Finite Fields Appl., 9, 2, 187-193, (2003) · Zbl 1081.11077
[2] Li, N.; Helleseth, T.; Tang, X., Further results on a class of permutation polynomials over finite fields, Finite Fields Appl., 22, 4, 16-23, (2013) · Zbl 1285.05004
[3] Lidl, R.; Niederreiter, H., Finite fields, Encycl. Math. Appl., vol. 20, (1997), Cambridge University Press Cambridge
[4] Tu, Z.; Zeng, X.; Jiang, Y., Two classes of permutation polynomials having the form \((x^{2^m} + x + \delta)^s + x\), Finite Fields Appl., 31, 12-24, (2015) · Zbl 1320.11120
[5] Yuan, J.; Ding, C., Four classes of permutation polynomials of \(\mathbb{F}_{2^m}\), Finite Fields Appl., 13, 4, 869-876, (2007) · Zbl 1167.11045
[6] Yuan, J.; Ding, C.; Wang, H.; Pieprzyk, J., Permutation polynomials of the form \((x^p - x + \delta)^s + L(x)\), Finite Fields Appl., 14, 2, 482-493, (2008) · Zbl 1211.11136
[7] Yuan, P.; Ding, C., Further results on permutation polynomials over finite fields, Finite Fields Appl., 27, 3, 88-103, (2014) · Zbl 1297.11148
[8] Zeng, X.; Zhu, X.; Hu, L., Two new permutation polynomials with the form \((x^{2^k} + x + \delta)^s + x\) over \(\mathbb{F}_{2^n}\), Appl. Algebra Eng. Commun. Comput., 21, 2, 145-150, (2010) · Zbl 1215.11116
[9] Zha, Z.; Hu, L., Two classes of permutation polynomials over finite fields, Finite Fields Appl., 18, 4, 781-790, (2012) · Zbl 1288.11111
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