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The Construction and Determination of Irreducible Polynomials Over Finite Fields

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Book cover Advances in Swarm Intelligence (ICSI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9713))

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Abstract

The approach for constructing the irreducible polynomials of arbitrary degree n over finite fields which is based on the number of the roots over the extension field is presented. At the same time, this paper includes a sample to illustrate the specific construction procedures. Then in terms of the relationship between the order of a polynomial over finite fields and the order of the multiplicative group of the extension field, a method which can determine whether a polynomial over finite fields is irreducible or not is proposed. By applying the Euclidean Algorithm, this judgment can be verified easily.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (61373150, 11501343), the Key Technologies R&D Program of Shaanxi Province (2013k0611), and the Fundamental Research Funds for the Central Universities (GK201603087).

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Authors and Affiliations

  1. School of Computer Science, Shaanxi Normal University, Xi’an, 710062, China

    Yun Song

  2. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Zhihui Li

Authors
  1. Yun Song
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  2. Zhihui Li
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Correspondence to Zhihui Li .

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Editors and Affiliations

  1. Peking University, Beijing, China

    Ying Tan

  2. Xi'an Jiaotong-Liverpool University, Suzhou, China

    Yuhui Shi

  3. Shenzen University, Shenzhen, China

    Li Li

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Song, Y., Li, Z. (2016). The Construction and Determination of Irreducible Polynomials Over Finite Fields. In: Tan, Y., Shi, Y., Li, L. (eds) Advances in Swarm Intelligence. ICSI 2016. Lecture Notes in Computer Science(), vol 9713. Springer, Cham. https://doi.org/10.1007/978-3-319-41009-8_67

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  • DOI: https://doi.org/10.1007/978-3-319-41009-8_67

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41008-1

  • Online ISBN: 978-3-319-41009-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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