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Nonlinear Feedforward Sequences of m-Sequences II

  • Zongduo Dai
  • Xuning Feng
  • Mulan Liu
  • Zhe-Xian Wan
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 20)

Abstract

Let
$$ \alpha \; = \;\left( {a_0 ,a_1 ,a_2 , \ldots } \right) $$
be a given n-stage m-sequence over the binary field F2, whose minimal polynomial will be denoted by f(x). We know that f(x) is primitive and of degree n. Denote \({{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{s}}}_{i}} = ({{a}_{i}},{{a}_{{i + 1}}}, \ldots ,{{a}_{{i + n - 1}}})\), i ≥ 0 and call \({{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{s}}}_{i}}\) the i-th state of the n-stage m-sequence α. Let
$$\phi \; = \;\sum\limits_{i_1 ,i_2 , \ldots ,i_n = 0}^1 {a_{i_1 \;i_2 \ldots i_n } } \;x_1^{i_1 } x_2^{i_2 } \ldots x_n^{i_n } ,\;a_{i_1 \;i_2 \ldots i_n } \; \in \;{\text{F}}_{\text{2}},$$
be a Boolean polynomial in n variables x 1,..., x n and of degree r. Obviously r ≤ n.

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References

  1. [1]
    Dai, Z., Feng, X., Liu, M. and Wan, Z., Nonlinear feedforward sequences of m-sequences, Proc. of 1988 Beijing International Workshop on Information Theory, July 4–7 (1988), A-2.1-A-2.8.Google Scholar
  2. [2]
    Zierler, N., Linear recurring sequences, J. Soc. Indust. Appl. Math., 7 (1959) 31–48.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1990

Authors and Affiliations

  • Zongduo Dai
    • 1
  • Xuning Feng
    • 2
  • Mulan Liu
    • 3
  • Zhe-Xian Wan
    • 3
  1. 1.Graduate SchoolAcademia SinicaBeijingPeople’s Republic of China
  2. 2.Institute of MathematicsAcademia SinicaBeijingPeople’s Republic of China
  3. 3.Institute of Systems ScienceAcademia SinicaBeijingPeople’s Republic of China

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