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More classes of permutation polynomials of the form \((x^{p^m}-x+\delta)^s+L(x)\). (English) Zbl 1366.05005

Summary: This note presents two classes of permutation polynomials of the form \((x^{p^m}-x+\delta)^s+L(x)\) over the finite fields \(\mathbb {F}_{p^{2m}}\) as a supplement of the recent works of Z. Zha and L. Hu [Finite Fields Appl. 18, No. 4, 781–790 (2012; Zbl 1288.11111); ibid. 40, 150–162 (2016; Zbl 1336.05005)] and N. Li et al. [ibid. 22, 16–23 (2013; Zbl 1285.05004)].

MSC:

11T06 Polynomials over finite fields
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[9] Yuan, J., Ding, C., Wang, H., Pieprzyk, J.: Permutation polynomials of the form \[(x^p-x +\delta )^s+L(x)\](xp-x+δ)s+L(x). Finite Fields Appl. 14(2), 482-493 (2008) · Zbl 1211.11136 · doi:10.1016/j.ffa.2007.05.003
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[14] Zeng, X., Zhu, X., Hu, L.: Two new permutation polynomials with the form \[(x^{2^k}+x +\delta )^s+x\](x2k+x+δ)s+x over \[{\mathbb{F}}_{2^n}\] F2n. Appl. Algebra Eng. Commun. Comput. 21(2), 145-150 (2010) · Zbl 1215.11116 · doi:10.1007/s00200-010-0120-6
[15] Zha, Z., Hu, L.: Two classes of permutation polynomials over finite fields. Finite Fields Appl. 18(4), 781-790 (2012) · Zbl 1288.11111 · doi:10.1016/j.ffa.2012.02.003
[16] Zha, Z., Hu, L.: Some classes of permutation polynomials of the form \[(x^{p^m}-x +\delta )^s+x\](xpm-x+δ)s+x over \[{\mathbb{F}}_{p^{2m}}\] Fp2m. Finite Fields Appl. 40, 150-162 (2016) · Zbl 1336.05005 · doi:10.1016/j.ffa.2016.04.003
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