Top

Applicable Algebra in Engineering, Communication and Computing

Published in:

30-09-2016 | Original Paper

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

Authors: Dabin Zheng, Zhen Chen

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 3/2017

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

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.

previous article On the dynamics of endomorphisms of finite groups

next article An automatic semigroup of languages

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Akbary, A., Ghioca, D., Wang, Q.: On constructing permutations of finite fields. Finite Fields Appl. 17(1), 51–67 (2011)MathSciNetCrossRefMATH

Helleseth, T., Zinoviev, V.: New Kloosterman sums identities over \(\mathbb{F}_{2^m}\) for all \(m\). Finite Fields Appl. 9(2), 187–193 (2003)MathSciNetCrossRefMATH

Li, N., Helleseth, T., Tang, X.: Further results on a class of permutation polynomials over finite fields. Finite Fields Appl. 22, 16–23 (2013)MathSciNetCrossRefMATH

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)MathSciNetCrossRefMATH

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)MathSciNetCrossRefMATH

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)MathSciNetCrossRefMATH

Yuan, J., Ding, C.: Four classes of permutation polynomials of \({\mathbb{F}}_{2^m}\). Finite Fields Appl. 13(4), 869–876 (2007)MathSciNetCrossRefMATH

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)MathSciNetCrossRefMATH

10.

Yuan, P., Ding, C.: Permutation polynomials over finite fields from a powerful lemma. Finite Fields Appl. 17(6), 560–574 (2011)MathSciNetCrossRefMATH

11.

Yuan, P., Ding, C.: Further results on permutation polynomials over finite fields. Finite Fields Appl. 27, 88–103 (2014)MathSciNetCrossRefMATH

12.

Yuan, P., Zheng, Y.: Permutation polynomials from piecewise functions. Finite Fields Appl. 35, 215–230 (2015)MathSciNetCrossRefMATH

13.

Zeng, X., Tian, S., Tu, Z.: Permutation polynomials from trace functions over finite fields. Finite Fields Appl. 35, 36–51 (2015)MathSciNetCrossRefMATH

14.

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)MathSciNetCrossRefMATH

15.

Zha, Z., Hu, L.: Two classes of permutation polynomials over finite fields. Finite Fields Appl. 18(4), 781–790 (2012)MathSciNetCrossRefMATH

16.

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)MathSciNetCrossRefMATH

Title: More classes of permutation polynomials of the form
Authors: Dabin Zheng
Zhen Chen
Publication date: 30-09-2016
Publisher: Springer Berlin Heidelberg
Published in: Applicable Algebra in Engineering, Communication and Computing / Issue 3/2017
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-016-0305-8

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 3/2017

Predicting the elliptic curve congruential generator

Polynomial interpolation of the Naor–Reingold pseudo-random function

On the dynamics of endomorphisms of finite groups

Affine equivalence and non-linearity of permutations over

An automatic semigroup of languages

Premium Partner