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Explicit Factorizations of Cyclotomic and Dickson Polynomials over Finite Fields

  • Robert W. Fitzgerald
  • Joseph L. Yucas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)

Abstract

We give, over a finite field F q , explicit factorizations into a product of irreducible polynomials, of the cyclotomic polynomials of order 3·2 n , the Dickson polynomials of the first kind of order 3·2 n and the Dickson polynomials of the second kind of order 3·2 n  − 1.

Keywords

finite field cyclotomic polynomial Dickson polynomial 

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References

  1. Alaca, Ş.: Congruences for Brewer sums. Finite Fields Appl. 13, 1–19 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  2. Fitzgerald, R.W., Yucas, J.L.: Factors of Dickson polynomials over finite fields. Finite Fields Appl. 11, 724–737 (2005)CrossRefMathSciNetGoogle Scholar
  3. Fitzgerald, R.W., Yucas, J.L.: A generalization of Dickson polynomials via linear fractional transformations. Int. J. Math. Comput. Sci. 1, 391–416 (2006)zbMATHMathSciNetGoogle Scholar
  4. Lidl, R., Niederreiter, H.: Finite Fields. In: Encyclopedia of Mathematics and Its Applications, 2nd edn., vol. 20, Cambridge University Press, Cambridge (1997)Google Scholar
  5. Meyn, H.: Factorization of the cyclotomic polynomial \(x^{2^n}+1\) over finite fields. Finite Fields Appl. 2, 439–442 (1996)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Robert W. Fitzgerald
    • 1
  • Joseph L. Yucas
    • 1
  1. 1.Southern Illinois University Carbondale 

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