Research Article | Open Access
Amir Akbary, Qiang Wang, "On Polynomials of the Form ", International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 023408, 7 pages, 2007. https://doi.org/10.1155/2007/23408
On Polynomials of the Form
We give a general criterion for permutation polynomials of the form , where , and . We employ this criterion to characterize several classes of permutation polynomials.
- R. Lidl and H. Niederreiter, Finite Fields, vol. 20 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, UK, 2nd edition, 1997.
- R. Lidl and G. L. Mullen, “When does a polynomial over a finite field permute the elements of the field?” The American Mathematical Monthly, vol. 95, no. 3, pp. 243–246, 1988.
- R. Lidl and G. L. Mullen, “When does a polynomial over a finite field permute the elements of the field?, II,” The American Mathematical Monthly, vol. 100, no. 1, pp. 71–74, 1993.
- G. L. Mullen, “Permutation polynomials over finite fields,” in Finite Fields, Coding Theory, and Advances in Communications and Computing, vol. 141, pp. 131–151, Marcel Dekker, New York, NY, USA, 1993.
- D. Q. Wan and R. Lidl, “Permutation polynomials of the form and their group structure,” Monatshefte für Mathematik, vol. 112, no. 2, pp. 149–163, 1991.
- H. Niederreiter and K. H. Robinson, “Complete mappings of finite fields,” Journal of the Australian Mathematical Society. Series A, vol. 33, no. 2, pp. 197–212, 1982.
- D. Wan, “Permutation polynomials over finite fields,” Acta Mathematica Sinica (New Series), vol. 10, pp. 30–35, 1994.
- L. E. Dickson, Linear Groups: With An Exposition of the Galois Field Theory, Dover, New York, NY, USA, 1958.
- Y. Laigle-Chapuy, “Permutation polynomials and applications to coding theory,” Finite Fields and Their Applications, vol. 13, no. 1, pp. 58–70, 2007.
- A. Akbary and Q. Wang, “A generalized Lucas sequence and permutation binomials,” Proceedings of the American Mathematical Society, vol. 134, no. 1, pp. 15–22, 2006.
- A. Akbary, S. Alaric, and Q. Wang, “On some classes of permutation polynomials,” to appear in International Journal of Number Theory.
Copyright © 2007 Amir Akbary and Qiang Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.