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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 \(2^{k}\).

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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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Authors and Affiliations

  1. Educationals University, Esfahan, Iran

    Saeid Mehrabi

  2. Institute for Informatics and Automation Problems, Armenia National Academy of Sciences, Yerevan, Armenia

    Melsik K. Kyuregyan

Authors
  1. Saeid Mehrabi
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  2. Melsik K. Kyuregyan
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Correspondence to Saeid Mehrabi.

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Mehrabi, S., Kyuregyan, M.K. Irreducible compositions of polynomials over finite fields of even characteristic. AAECC 23, 207–220 (2012). https://doi.org/10.1007/s00200-012-0175-7

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  • DOI: https://doi.org/10.1007/s00200-012-0175-7

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