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Further results on permutation polynomials of the form \((x^{p^m}-x+\delta)^s+x\) over \(\mathbb{F}_{p^{2m}}\). (English) Zbl 1400.11155
Summary: Let \(\mathbb{F}_q\) denote the finite field of order \(q\). In this paper, some new classes of permutation polynomials of the form \((x^{p^m} - x + \delta)^s + x\) over \(\mathbb{F}_{p^{2 m}}\) are obtained by determining the number of solutions of certain equations.

MSC:
11T06 Polynomials over finite fields
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[1] Ding, C.; Helleseth, T., Optimal ternary cyclic codes from monomials, IEEE Trans. Inf. Theory, 59, 5898-5904, (2013) · Zbl 1364.94652
[2] Ding, C.; Yuan, J., A family of skew Hadamard difference sets, J. Comb. Theory, Ser. A, 113, 1526-1535, (2006) · Zbl 1106.05016
[3] Helleseth, T.; Zinoviev, V., New Kloosterman sums identities over \(\mathbb{F}_{2^m}\) for all m, Finite Fields Appl., 9, 187-193, (2003) · Zbl 1081.11077
[4] Hou, X., Permutation polynomials over finite fields - a survey of recent advances, Finite Fields Appl., 32, 82-119, (2015) · Zbl 1325.11128
[5] Laigle-Chapuy, Y., Permutation polynomials and applications to coding theory, Finite Fields Appl., 13, 58-70, (2007) · Zbl 1107.11048
[6] Li, N.; Helleseth, T.; Tang, X., Further results on a class of permutation polynomials over finite fields, Finite Fields Appl., 22, 16-23, (2013) · Zbl 1285.05004
[7] Lidl, R.; Muller, W. B., Permutation polynomials in RSA-cryptosystems, (Advances in Cryptology, (1984), Plenum New York), 293-301
[8] Schwenk, J.; Huber, K., Public key encryption and digital signatures based on permutation polynomials, Electron. Lett., 34, 759-760, (1998)
[9] 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
[10] Tu, Z.; Zeng, X.; Li, C.; Helleseth, T., 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, Finite Fields Appl., 34, 20-35, (2015) · Zbl 1315.05008
[11] Wang, L.; Wu, B.; Liu, Z., Further results on permutation polynomials of the form \((x^{p^m} - x + \delta)^s + L(x)\) over \(\mathbb{F}_{p^{2 m}}\), Finite Fields Appl., 44, 92-112, (2017) · Zbl 1352.05009
[12] Xu, G.; Cao, X.; Xu, S., Further results on permutation polynomials of the form \((x^{p^m} - x + \delta)^s + L(x)\) over \(\mathbb{F}_{p^{2 m}}\), J. Algebra Appl., 15, (2016) · Zbl 1334.05004
[13] Yuan, J.; Ding, C., Four classes of permutation polynomials of \(\mathbb{F}_{2^m}\), Finite Fields Appl., 13, 869-876, (2007) · Zbl 1167.11045
[14] Yuan, J.; Ding, C.; Wang, H.; Pieprzyk, J., Permutation polynomials of the form \((x^p - x + \delta)^s + L(x)\), Finite Fields Appl., 14, 482-493, (2008) · Zbl 1211.11136
[15] Yuan, P.; Ding, C., Permutation polynomials over finite fields from a powerful lemma, Finite Fields Appl., 17, 560-574, (2011) · Zbl 1258.11100
[16] Yuan, P.; Ding, C., Further results on permutation polynomials over finite fields, Finite Fields Appl., 27, 88-103, (2014) · Zbl 1297.11148
[17] Yuan, P.; Zheng, Y., Permutation polynomials from piecewise functions, Finite Fields Appl., 35, 215-230, (2015) · Zbl 1331.11108
[18] 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, 145-150, (2010) · Zbl 1215.11116
[19] Zha, Z.; Hu, L., Two classes of permutation polynomials over finite fields, Finite Fields Appl., 18, 781-790, (2012) · Zbl 1288.11111
[20] Zha, Z.; Hu, L., Some classes of permutation polynomials of the form \((x^{p^m} - x + \delta)^s + x\) over \(\mathbb{F}_{p^{2 m}}\), Finite Fields Appl., 40, 150-162, (2016) · Zbl 1336.05005
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