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Classification and counting on multi-continued fractions and its application to multi-sequences

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Abstract

In the light of multi-continued fraction theories, we make a classification and counting for multi-strict continued fractions, which are corresponding to multi-sequences of multiplicity m and length n. Based on the above counting, we develop an iterative formula for computing fast the linear complexity distribution of multi-sequences. As an application, we obtain the linear complexity distributions and expectations of multi-sequences of any given length n and multiplicity m less than 12 by a personal computer. But only results of m=3 and 4 are given in this paper.

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Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing, 100049, China

    Dai ZongDuo

  2. WatchData Research, Watchdata System Co. Ltd, YanDong Business Park, Capital Airport Road, Chaoyang District, Beijing, 100015, China

    Feng XiuTao

Authors
  1. Dai ZongDuo
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  2. Feng XiuTao
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Corresponding author

Correspondence to Feng XiuTao.

Additional information

Supported partly by the National Natural Science Foundation of China (Grants Nos. 60173016 and 90604011)

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Dai, Z., Feng, X. Classification and counting on multi-continued fractions and its application to multi-sequences. SCI CHINA SER F 50, 351–358 (2007). https://doi.org/10.1007/s11432-007-0032-7

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  • DOI: https://doi.org/10.1007/s11432-007-0032-7

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