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Mathematical Problems of Computer Science 31, 16-27, 2008. 

16 
 

 
Completely Normal Elements in Iterated Quadratic Extensions 

of Finite Fields of Odd Characteristics 
 

Melsik K. Kyuregyan and Ofelya A. Manukyan 
 

Institute for Informatics and Automation Problems, Armenian National Academy of Sciences 
E-mails: melsik@ipia.sci.am, manofa81@yahoo.com 

 
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 
 
[1] R. Chapman, “Completely normal elements in iterated quadratic extensions of finite fields”, Finite 
Fields Appl., Volume 3, pp. 3-10, 1997. 
[2] S. D. Cohen, “The explicit construction of irreducible polynomials over finite fields”, Design, Codes 
and Cryptography, Volume 2, pp. 169-174, 1992. 
[3] M. K. Kyuregyan, “Recurrent methods for constructing irreducible polynomials over qF  of odd 
characteristics”, Finite Fields Appl., Volume 9, pp. 39-58, 2003. 
 

[4] 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. 
 
 
 

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