Constructing permutations and complete permutations over finite fields via subfield-valued polynomials

We describe a recursive construction of permutation and complete permutation polynomials over a finite field F p n by using F p k -valued polynomials for several same or different factors k of n. As a result, we obtain some specific permutation polynomials which unify and generalize several previous constructions.

[1]  Qiang Wang,et al.  On constructing permutations of finite fields , 2011, Finite Fields Their Appl..

[2]  Qiang Wang,et al.  On the inverses of some classes of permutations of finite fields , 2013, Finite Fields Their Appl..

[3]  Lei Hu,et al.  Several classes of complete permutation polynomials , 2014, Finite Fields Their Appl..

[4]  Ulrich Dempwolff,et al.  Permutation polynomials and translation planes of even order , 2012 .

[5]  Henk D. L. Hollmann,et al.  A class of permutation polynomials of F2m related to Dickson polynomials , 2005, Finite Fields Their Appl..

[6]  Xiang-dong Hou,et al.  A piecewise construction of permutation polynomials over finite fields , 2012, Finite Fields Their Appl..

[7]  Tor Helleseth,et al.  New Kloosterman sums identities over F2m for all m , 2003 .

[8]  Michael E. Zieve.  Classes of Permutation Polynomials Based on Cyclotomy and an Additive Analogue , 2008, 0810.2830.

[9]  Cunsheng Ding,et al.  Permutation polynomials over finite fields from a powerful lemma , 2011, Finite Fields Their Appl..

[10]  Gohar M. M. Kyureghyan.  Constructing permutations of finite fields via linear translators , 2009, J. Comb. Theory, Ser. A.

[11]  José E. Marcos,et al.  Specific permutation polynomials over finite fields , 2008, Finite Fields Their Appl..

[12]  Rudolf Lide,et al.  Finite fields , 1983 .

[13]  Baofeng Wu,et al.  The compositional inverse of a class of bilinear permutation polynomials over finite fields of characteristic 2 , 2013, Finite Fields Their Appl..

[14]  Lei Hu,et al.  New methods for generating permutation polynomials over finite fields , 2011, Finite Fields Their Appl..

[15]  Tor Helleseth,et al.  Some classes of monomial complete permutation polynomials over finite fields of characteristic two , 2014, Finite Fields Their Appl..

[16]  Cunsheng Ding,et al.  Permutation polynomials of the form L(x) + Sa2k + Sb2k over 𝔽q3k , 2014, Finite Fields Their Appl..

[17]  Wang Daqing,et al.  Permutation polynomials over finite fields , 1987 .

[18]  Pascale Charpin,et al.  When does G(x)+gammaTr(H(x)) permute Fpn? , 2009, Finite Fields Their Appl..

[19]  Lei Hu,et al.  Two classes of permutation polynomials over finite fields , 2012, Finite Fields Their Appl..

[20]  Cunsheng Ding,et al.  Further results on permutation polynomials over finite fields , 2013, Finite Fields Their Appl..

[21]  Cunsheng Ding,et al.  Four classes of permutation polynomials of F2m , 2007, Finite Fields Their Appl..

[22]  H. Niederreiter,et al.  Complete mappings of finite fields , 1982, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[23]  Qiang Wang,et al.  Cyclotomy and permutation polynomials of large indices , 2012, Finite Fields Their Appl..

[24]  Lei Hu,et al.  Two new permutation polynomials with the form $${\left(x^{2^k}+x+\delta\right)^{s}+x}$$ over $${\mathbb{F}_{2^n}}$$ , 2010, Applicable Algebra in Engineering, Communication and Computing.

[25]  Xiang-Dong Hou,et al.  A new approach to permutation polynomials over finite fields , 2012, Finite Fields Their Appl..

[26]  Yann Laigle-Chapuy,et al.  Permutation polynomials and applications to coding theory , 2007, Finite Fields Their Appl..

[27]  Josef Pieprzyk,et al.  Permutation polynomials of the form (xp-x+delta)s+L(x) , 2008, Finite Fields Their Appl..