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International Workshop on Computer Algebra in Scientific Computing

CASC 2019: Computer Algebra in Scientific Computing pp 362–376Cite as

On Berlekamp–Massey and Berlekamp–Massey–Sakata Algorithms

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11661))

Abstract

The Berlekamp–Massey and Berlekamp–Massey–Sakata algorithms compute a minimal polynomial or polynomial set of a linearly recurring sequence or multi-dimensional array. In this paper some underlying properties of and connections between these two algorithms are clarified theoretically: a unified flow chart for both algorithms is proposed to reveal their connections; the polynomials these two algorithms maintain at each iteration are proved to be reciprocal when both algorithms are applied to the same sequence; and the uniqueness of the choices of polynomials from two critical polynomial sets in the Berlekamp–Massey–Sakata algorithm is investigated.

This work was partially supported by the National Natural Science Foundation of China (NSFC 11771034) and the Fundamental Research Funds for the Central Universities in China (YWF-19-BJ-J-324).

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Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful suggestion which contribute to considerable improvement of this paper.

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Authors and Affiliations

  1. LMIB–School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China

    Chenqi Mou & Xiaolin Fan

  2. Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China

    Chenqi Mou

Authors
  1. Chenqi Mou
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  2. Xiaolin Fan
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Corresponding author

Correspondence to Chenqi Mou .

Editor information

Editors and Affiliations

  1. Coventry University, Coventry, UK

    Matthew England

  2. University of Kassel, Kassel, Germany

    Wolfram Koepf

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. University of Kassel, Kassel, Germany

    Werner M. Seiler

  5. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Mou, C., Fan, X. (2019). On Berlekamp–Massey and Berlekamp–Massey–Sakata Algorithms. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_24

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  • DOI: https://doi.org/10.1007/978-3-030-26831-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26830-5

  • Online ISBN: 978-3-030-26831-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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