论文信息 - On inverse permutation polynomials

On inverse permutation polynomials

We give an explicit formula of the inverse polynomial of a permutation polynomial of the form x^rf(x^s) over a finite field F"q where s|q-1. This generalizes results in [A. Muratovic-Ribic, A note on the coefficients of inverse polynomials, Finite Fields Appl. 13 (4) (2007) 977-980] where s=1 or f=g^q^-^1^s were considered respectively. We also apply our result to several interesting classes of permutation polynomials.

Qiang Wang

[1] Qiang Wang,et al. Research Article On Polynomials of the Form x r f(x (q−1)/l ) , 2007 .

[2] Qiang Wang,et al. A generalized Lucas sequence and permutation binomials , 2005 .

[3] Rudolf Lidl,et al. Permutation polynomials of the formxrf(xq−1)/d) and their group structure , 1991 .

[4] Qiang Wang,et al. On Polynomials of the Form xrf(x(q-1)/l) , 2007, Int. J. Math. Math. Sci..

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

[6] Qiang Wang,et al. On permutation polynomials of prescribed shape , 2009, Finite Fields Their Appl..

[7] Qiang Wang,et al. On some permutation polynomials over finite fields , 2005, Int. J. Math. Math. Sci..

[8] Qiang Wang,et al. Cyclotomic Mapping Permutation Polynomials over Finite Fields , 2007, SSC.

[9] Amela Muratovic-Ribic. A note on the coefficients of inverse polynomials , 2007, Finite Fields Their Appl..