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Acta Mathematica Sinica

, Volume 4, Issue 1, pp 55–63 | Cite as

A relationship between the Berlekamp-Massey and the euclidean algorithms for linear feedback shift register synthesis

  • Dai Zongduo
  • Wan Zhexian
Article

Abstract

A relationship between the Berlekamp-Massey and the Euclidean algorithms for linear feedback shift register synthesis is established. In fact, by refining a sequence of polynomials appearing in the Euclidean algorithm, the sequence of characteristic polynomials computed by the Berlekamp-Massey algorithm will be achieved.

Keywords

Characteristic Polynomial Arbitrary Element Linear Complexity Linear Feedback Shift Register Small Positive Integer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Dai Zongduo, Proof of Rueppel's Linear Complexity Conjecture, IEEE Transaction on Information Theory,IT-32 (1986), 440–443.CrossRefGoogle Scholar
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    Imamura, K., Two Recursive Algorithms for Solving the Scalar Partial Realization Problem, IEEE ISCAS 85, 823–824.Google Scholar
  3. [3]
    Massey, J.L., Shift Register Synthesis and BCH Decoding, IEEE Transactions of Information Theory,IT-15 (1969), 122–129.CrossRefMathSciNetGoogle Scholar
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    Mills, W.H., Continued Fractions and Linear Recurrences.Math. Comp.,29 (1975), 173–180.CrossRefMathSciNetGoogle Scholar
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    Sugiyama, Y., Kaschara, M., Hirasawa, S. and Namekawa, T., A Method for Solving Key Equation for Decoding Goppa Codes,Information and Control,29 (1975), 173–180.Google Scholar

Copyright information

© Science Press 1988

Authors and Affiliations

  • Dai Zongduo
    • 1
  • Wan Zhexian
    • 2
  1. 1.Institute of MathematicsAcademia SinicaChina
  2. 2.Department for Information TheoryUniversity of LundLundSwitzerland

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