Abstract
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 Zha, Hu and Li, Helleseth and Tang.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akbary, A., Ghioca, D., Wang, Q.: On constructing permutations of finite fields. Finite Fields Appl. 17(1), 51–67 (2011)
Helleseth, T., Zinoviev, V.: New Kloosterman sums identities over \(\mathbb{F}_{2^m}\) for all \(m\). Finite Fields Appl. 9(2), 187–193 (2003)
Li, N., Helleseth, T., Tang, X.: Further results on a class of permutation polynomials over finite fields. Finite Fields Appl. 22, 16–23 (2013)
Lidl, R., Niederreiter, H.: Finite fields. In: Encyclopedia of Mathematics and Its Applications, vol 20, 2nd edn. Cambridge University Press, Cambridge (1997)
Marcos, J.E.: Some permutation polynomials over finite fields. Appl. Algebra Eng. Commun. Comput. 26(5), 465–474 (2015)
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)
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 \({\mathbb{F}}_{p^{2m}}\) of odd characteristic. Finite Fields Appl. 34, 20–35 (2015)
Yuan, J., Ding, C.: Four classes of permutation polynomials of \({\mathbb{F}}_{2^m}\). Finite Fields Appl. 13(4), 869–876 (2007)
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)
Yuan, P., Ding, C.: Permutation polynomials over finite fields from a powerful lemma. Finite Fields Appl. 17(6), 560–574 (2011)
Yuan, P., Ding, C.: Further results on permutation polynomials over finite fields. Finite Fields Appl. 27, 88–103 (2014)
Yuan, P., Zheng, Y.: Permutation polynomials from piecewise functions. Finite Fields Appl. 35, 215–230 (2015)
Zeng, X., Tian, S., Tu, Z.: Permutation polynomials from trace functions over finite fields. Finite Fields Appl. 35, 36–51 (2015)
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)
Zha, Z., Hu, L.: Two classes of permutation polynomials over finite fields. Finite Fields Appl. 18(4), 781–790 (2012)
Zha, Z., Hu, L.: Some classes of permutation polynomials of the form \((x^{p^m}-x +\delta )^s+x\) over \({\mathbb{F}}_{p^{2m}}\). Finite Fields Appl. 40, 150–162 (2016)
Acknowledgments
The authors wish to thank the anonymous referees for their helpful comments. The work was partially supported by National Natural Science Foundation of China (NSFC) under Grant 11101131.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zheng, D., Chen, Z. More classes of permutation polynomials of the form \((x^{p^m}-x+\delta )^s+L(x)\) . AAECC 28, 215–223 (2017). https://doi.org/10.1007/s00200-016-0305-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00200-016-0305-8