Completely Normal Elements in Iterated Quadratic Extensions of Finite Fields of Odd Characteristics

Authors

  • Melsik K. Kyuregyan Institute for Informatics and Automation Problems of NAS RA
  • Ofelya A. Manukyan Institute for Informatics and Automation Problems of NAS RA

Abstract

In this paper computationally easy explicit constructions of sequences of irreducible and normal monic polynomials over finite fields of odd characteristic are presented.

References

R. Chapman, “Completely normal elements in iterated quadratic extensions of finite fields”, Finite Fields Appl., Volume 3, pp. 3-10, 1997.

S. D. Cohen, “The explicit construction of irreducible polynomials over finite fields”, Design, Codes and Cryptography, Volume 2, pp. 169-174, 1992.

M. K. Kyuregyan, “Recurrent methods for constructing irreducible polynomials over q F of odd characteristics”, Finite Fields Appl., Volume 9, pp. 39-58, 2003.

G. McNay, Topics in finite fields, Ph.D. Thesis, University of Glasgow, 1995.[5] A. J. Menezes, I. F. Blake, X. Gao, R. C. Mullin, S. A. Vanstone, T. Yaghoobian, “Applications of Finite Fields”, Kluwer Publishers, Boston, Dordrecht, Lancaster, 1993.[6] H. Meyn, “Explicit N-polynomials of 2-power degree over finite fields”, I, Designs, Codes and Cryptography, Volume 6, pp. 107-116, 1995.

A.J. Menezes, I.F. Blake, X. Gao, R.C. Mullin, S.A. Vanstone, T.Yaghoobian, “Applications of Finite Fields”, Kluwer Publishers, Boston, Dordrecht, Lancaster, 1993.

H. Meyn, “Explicit N-polynomials of 2-power degree over finite fields”, I, Designs, Codes and Cryptography, Volume 6, pp. 107-116, 1995.

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Published

2008-09-25

How to Cite

Kyuregyan, M. K. ., & Manukyan, O. A. . (2008). Completely Normal Elements in Iterated Quadratic Extensions of Finite Fields of Odd Characteristics. Mathematical Problems of Computer Science, 31, 16–27. Retrieved from https://mpcs.sci.am/index.php/mpcs/article/view/388