Linear Complexity of Periodically Repeated Random Sequences

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 547)


On the linear complexity Λ(\( \tilde z \)) of a periodically repeated random bit sequence \( \tilde z \), R. Rueppel proved that, for two extreme cases of the period T, the expected linear complexity E[Λ(\( \tilde z \))] is almost equal to T, and suggested that E[Λ(\( \tilde z \))] would be close to T in general [6, pp. 33–52] [7, 8]. In this note we obtain bounds of E[Λ(\( \tilde z \))], as well as bounds of the variance V ar[Λ(\( \tilde z \))], both for the general case of T, and we estimate the probability distribution of Λ(\( \tilde z \)). Our results on E[Λ(\( \tilde z \))] quantify the closeness of E[Λ(\( \tilde z \))] and T, in particular, formally confirm R. Rueppel’s suggestion.


Linear Complexity Random Sequences 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  1. 1.Dept. of Math., RHBNCUniversity of LondonEgham, SurreyUK
  2. 2.Computing CenterAcademia SinicaBeijingChina

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