Abstract
The paper is devoted to the composition method of constructing families of irreducible polynomials over finite fields.
Similar content being viewed by others
References
Albert A.A.: Fundamental Concepts of Higher Algebra. University of Chicago Press, Chicago (1956)
Chapman R.: Completely normal elements in iterated quadratic extensions of finite fields. Finite Fields Appl. 3, 3–10 (1997)
Cohen S.D.: On irreducible polynomials of certain types in finite fields. Proc. Cambridge Philos. Soc. 66, 335–344 (1969)
Cohen S.D.: The explicit construction of irreducible polynomials over finite fields. Des. Codes Cryptogr. 2, 169–173 (1992)
Cohen S.D.: Explicit theorems on generator polynomials. Finite Fields Appl. 11, 337–357 (2005)
Kyuregyan M.K.: Recurrent methods for constructing irreducible polynomials over \({\mathbb{F}_q}\) of odd characteristics. Finite Fields Appl. 9, 39–58 (2003)
Kyuregyan M.K.: Iterated constructions of irreducible polynomials over finite fields with linearly independent roots. Finite Fields Appl. 10, 323–431 (2004)
Kyuregyan M.K.: Recurrent methods for constructing irreducible polynomials over \({\mathbb{F}_q}\) of odd characteristics II. Finite Fields Appl. 12, 357–378 (2006)
Kyuregyan M.K., Evoyan M.G.: Two methods for constructing irreducible polynomials over finite fields based on polynomial composition. In: Proceedings of CSIT 2009, Yerevan, Armenia. http://www.csit.am/2009/proceedings/3ITCT/17.pdf (2009).
Lidl R., Niederreiter H.: Finite Fields. Cambridge University Press, Cambridge (1987)
McNay G.: Topics in finite fields. Ph.D. Thesis, University of Glasgow (1995).
Meyn H.: Explicit N-polynomials of 2-power degree over finite fields. Des. Codes Cryptogr. 6, 107–116 (1995)
Menezes A., Blake I.F., Gao X., Mullin R.C., Vanstone S.A., Yaghoobian T.: Applications of Finite Fields. Kluwer Academic Publishers, Boston (1993)
Scheerhorn A.: Iterated constructions of normal bases over finite fields. In: Mullen G.L., Shiue P.J.-S. (eds.) Finite Fields: Theory, Applications and Algorithms, Contemporary Mathematics, American Mathematical Society, Providence, RI (1994).
Sidelnikov V.M.: On normal bases of a finite field. Sb. Math. USSR 61, 485–494 (1988)
Varshamov R.R.: A general method of synthesizing irreducible polynomials over Galois fields. Dokl. Math. USSR 29, 334–336 (1984)
Zierler N.: Linear recurring sequences. J. Soc. Ind. Appl. Math. 7, 31–48 (1959)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by S. Gao.
Rights and permissions
About this article
Cite this article
Kyuregyan, M.K., Kyureghyan, G.M. Irreducible compositions of polynomials over finite fields. Des. Codes Cryptogr. 61, 301–314 (2011). https://doi.org/10.1007/s10623-010-9478-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-010-9478-5