Irreducible compositions of polynomials over finite fields of even characteristic

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Abstract

This paper presents some results with the constructive theory of synthesis of irreducible polynomials over a Galois field with even characteristic. We prove a theorem that plays an important role for constructing irreducible polynomials. By this theorem two recurrent methods for constructing families of irreducible polynomials of degree \(n2^{k}~(k=1,2,\ldots )\) over \(\mathbb F _{2^{s}}\) are proposed. It is shown that in this special case, the sequences of irreducible polynomials are N-polynomial of degree \(2^{k}\).

Keywords

Galois fields Irreducible polynomials Recurrent method  N-polynomial 
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Notes

Acknowledgments

We would like to thank the anonymous referee for carefully reading our manuscript and for his very detailed comments. His many helpful suggestions and corrections allowed us to improve the presentation of the paper and improve its readability.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Educationals UniversityEsfahanIran
  2. 2.Institute for Informatics and Automation ProblemsArmenia National Academy of SciencesYerevanArmenia

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