International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2007 / Article

Research Article | Open Access

Volume 2007 |Article ID 023408 | https://doi.org/10.1155/2007/23408

Amir Akbary, Qiang Wang, "On Polynomials of the Form xrf(x(q1)/l)", 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 xrf(x(q1)/l)

Academic Editor: Nils-Peter Skoruppa
Received23 Jul 2007
Accepted29 Oct 2007
Published31 Jan 2008

Abstract

We give a general criterion for permutation polynomials of the form xrf(x(q1)/l), where r1, l1 and l(q1). We employ this criterion to characterize several classes of permutation polynomials.

References

  1. R. Lidl and H. Niederreiter, Finite Fields, vol. 20 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, UK, 2nd edition, 1997. View at: MathSciNet
  2. 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. View at: Publisher Site | Google Scholar | MathSciNet
  3. 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. View at: Publisher Site | Google Scholar | MathSciNet
  4. 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. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  5. D. Q. Wan and R. Lidl, “Permutation polynomials of the form xrf(x(q1)/d) and their group structure,” Monatshefte für Mathematik, vol. 112, no. 2, pp. 149–163, 1991. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  6. 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. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  7. D. Wan, “Permutation polynomials over finite fields,” Acta Mathematica Sinica (New Series), vol. 10, pp. 30–35, 1994. View at: Google Scholar
  8. L. E. Dickson, Linear Groups: With An Exposition of the Galois Field Theory, Dover, New York, NY, USA, 1958. View at: MathSciNet
  9. Y. Laigle-Chapuy, “Permutation polynomials and applications to coding theory,” Finite Fields and Their Applications, vol. 13, no. 1, pp. 58–70, 2007. View at: Publisher Site | Google Scholar | MathSciNet
  10. 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. View at: Publisher Site | Google Scholar | MathSciNet
  11. A. Akbary, S. Alaric, and Q. Wang, “On some classes of permutation polynomials,” to appear in International Journal of Number Theory. View at: Google Scholar

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.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views300
Downloads756
Citations

Related articles

Article of the Year Award: Outstanding research contributions of 2020, as selected by our Chief Editors. Read the winning articles.