Several Classes of Permutation Polynomials over Finite Fields

DOI: 10.4236/jcc.2014.24003   PDF   HTML     5,951 Downloads   7,618 Views  

Abstract

Several classes of permutation polynomials of the form  over finite fields are presented in this paper, which is a further investigation on a recent work of Li et al.

Share and Cite:

Sun, G. (2014) Several Classes of Permutation Polynomials over Finite Fields. Journal of Computer and Communications, 2, 18-24. doi: 10.4236/jcc.2014.24003.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Hermite, Ch. (1863) Sur les Fonctions de Sept Lettres. C.R. Acad. Sci. Paris, 57, 750-757.
[2] Dickson, L.E. (1896) The Analytic Representation of Substitutions on a power of a Prime Number of Letters with a Discussion of the Linear Group. Annals of Mathematics, 11, 65-120. http://dx.doi.org/10.2307/1967217
[3] Cohen, S.D. (1997) Permutation Group Theory and Permutation Polynomials. In: Algebra and Combinatorics, ICAC’97, Hong Kong, August 1997, 133-146.
[4] Laigle-Chapuy, Y. (2007) Permutation Polynomials and Applications to Coding Theory. Finite Fields and Their Applications, 13, 58-70. http://dx.doi.org/10.1016/j.ffa.2005.08.003
[5] Lidl, R. and Niederreiter, H. (1997) Finite fields. 2nd Edition, Cambridge University Press.
[6] Mullen, G.L. (1993) Permutation Polynomials over Finite Fields. Proceedings of Conference on Finite Fields and Their Applications, Lecture Notes in Pure and Applied Mathematics, Vol. 141, Marcel Dekker, New York, 131-151.
[7] Cao, X. and Hu, L. (2011) New Methods for Generating Permutation Polynomials over Finite Fields. Finite Fields and Their Applications, 17, 493-503. http://dx.doi.org/10.1016/j.ffa.2011.02.012
[8] Charpin, P. and Kyureghyan, G. (2009) When Does Permute . Finite Fields and Their Applications, 15, 615-632. http://dx.doi.org/10.1016/j.ffa.2009.07.001
[9] Ding, C., Xiang, Q., Yuan, J. and Yuan, P. (2009) Explicit Classes of Permutation Polynomials of . Science in China Series A: Mathematics, 53, 639-647. http://dx.doi.org/10.1007/s11425-008-0142-8
[10] Fernando, N., Hou, X. and Lappano, S. (2013) A New Approach to Permutation Polynomials over Finite Fields II. Finite Fields and Their Applications, 18, 492-521. http://dx.doi.org/10.1016/j.ffa.2013.01.001
[11] Hollmann, H.D.L. and Xiang, Q. (2005) A Class of Permutation Polynomials of Related to Dickson Polynomials. Finite Fields and Their Applications, 11, 111-122. http://dx.doi.org/10.1016/j.ffa.2004.06.005
[12] Hou, X. (2012) A New Approach to Permutation Polynomials over Finite Fields. Finite Fields and Their Applications, 18, 492-521. http://dx.doi.org/10.1016/j.ffa.2011.11.002
[13] Helleseth, T. and Zinoviev, V. (2003) New Kloosterman Sums Identities over for All . Finite Fields and Their Applications, 9, 187-193. http://dx.doi.org/10.1016/S1071-5797(02)00028-X
[14] Yuan, J. and Ding, C. (2007) Four Classes of Permutation Polynomials of . Finite Fields and Their Applications, 13, 869-876. http://dx.doi.org/10.1016/j.ffa.2006.05.006
[15] Yuan, J., Ding, C., Wang, H. and Pieprzyk, J. (2008) Permutation Polynomials of the Form . Finite Fields and Their Applications, 14, 482-493. http://dx.doi.org/10.1016/j.ffa.2007.05.003
[16] Yuan, P. and Ding, C. (2011) Permutation Polynomials over Finite Fields from a Powerful Lemma. Finite Fields and Their Applications, 17, 560-574. http://dx.doi.org/10.1016/j.ffa.2011.04.001
[17] Zeng, X., Zhu, X. and Hu, L. (2010) Two New Permutation Polynomials with the Form over . Applicable Algebra in Engineering, Communication and Computing, 21, 145-150.
[18] Zha, Z. and Hu, L. (2012) Two Classes of Permutation Polynomials over Finite Fields. Finite Fields and Their Applications, 18, 781-790. http://dx.doi.org/10.1016/j.ffa.2012.02.003
[19] Li, N., Helleseth, T. and Tang, X. (2013) Further Results on a Class of Permutation Polynomials over Finite Fields. Finite Fields and Their Applications, 22, 16-23.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.