Research PapersNo Access

New results on permutation polynomials over finite fields

Xiaoer Qin

Mathematical College, Sichuan University, Chengdu 610064, P. R. China

College of Mathematics and Computer Science, Yangtze Normal University, Chongqing 408100, P. R. China

Search for more papers by this author

Guoyou Qian

Mathematical College, Sichuan University, Chengdu 610064, P. R. China

Search for more papers by this author

, and

Shaofang Hong

Mathematical College, Sichuan University, Chengdu 610064, P. R. China

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S1793042115500220Cited by:6 (Source: Crossref)

Abstract

In this paper, we get several new results on permutation polynomials over finite fields. First, by using the linear translator, we construct permutation polynomials of the forms and . These forms generalize the results obtained by Kyureghyan in 2011. Consequently, we characterize permutation polynomials of the form , which extends a theorem of Charpin and Kyureghyan obtained in 2009.

Keywords:

AMSC: 11T06, 12E20

References

M. Ayad , K. Belghaba and O. Kihel , Bull. Aust. Math. Soc. 89 , 112 ( 2014 ) . Crossref, Web of Science, Google Scholar
P. Charpin and G. Kyureghyan, On a class of permutation polynomials over F2n, SETA 20085203, Lecture Notes in Computer Science (Springer, Berlin, 2008) pp. 368–376. Google Scholar
–– , Finite Fields Appl. 15 , 615 ( 2009 ) . Crossref, Web of Science, Google Scholar
M. Evoyan , G. Kyureghyan and M. Kyureghyan , Math. Probl. Comput. Sci. 39 , 5 ( 2013 ) . Google Scholar
X. Hou , J. Combin. Theory Ser. A 118 , 448 ( 2011 ) . Crossref, Web of Science, Google Scholar
G. Kyureghyan , J. Combin. Theory Ser. A 118 , 1052 ( 2011 ) . Crossref, Web of Science, Google Scholar
Y. Laigle-Chapuy , Finite Fields Appl. 13 , 58 ( 2007 ) . Crossref, Web of Science, Google Scholar
R. Lidl and G. L. Mullen , Amer. Math. Monthly 95 , 243 ( 1988 ) . Crossref, Web of Science, Google Scholar
R. Lidl and H. Niederreiter , Finite Fields , 2nd edn. , Encyclopedia of Mathematics and its Applications 20 ( Cambridge University Press , Cambridge , 1997 ) . Google Scholar
S. Ling and L. Qu , Finite Fields Appl. 18 , 56 ( 2012 ) . Crossref, Web of Science, Google Scholar
J. E. Marcos , Finite Fields Appl. 17 , 105 ( 2011 ) . Crossref, Web of Science, Google Scholar
A. Masuda and M. E. Zieve , Trans. Amer. Math. Soc. 361 , 4169 ( 2009 ) . Crossref, Web of Science, Google Scholar
X. Qin and S. Hong , Bull. Aust. Math. Soc. 89 , 420 ( 2014 ) . Crossref, Web of Science, Google Scholar
J. Schwenk and K. Huber , Electron. Lett. 34 , 759 ( 1998 ) . Crossref, Web of Science, Google Scholar
D. Wan and R. Lidl , Monatsh. Math. 112 , 149 ( 1991 ) . Crossref, Web of Science, Google Scholar
M. E. Zieve , Int. J. Number Theory 4 , 851 ( 2008 ) . Link, Web of Science, Google Scholar
M. E. Zieve , Proc. Amer. Math. Soc. 137 , 2209 ( 2009 ) . Crossref, Web of Science, Google Scholar
M. E. Zieve, Additive Number Theory (Springer, New York, 2010) pp. 355–361. Crossref, Google Scholar
M. E. Zieve, Permutation polynomials on Fq induced from Rdei function bijections on subgroups of Fq, preprint (2013) , arXiv:1310.0776 . Google Scholar
M. E. Zieve, Permutation polynomials induced from permutations of subfields, and some complete sets of mutually orthogonal Latin squares, preprint (2013) , arXiv:1312.1325 . Google Scholar