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The Hausdorff Dimension of the Set of r-Perfect M-Multisequences

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Sequences and Their Applications – SETA 2006 (SETA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4086))

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Abstract

We introduce a stochastic infinite state machine (Markov chain) BDM, the “Battery–Discharge–Model”, which keeps track of all linear complexities of all q M.n prefixes of length n of M-multisequences over \({\mathbb {F}}_q\).

We then use a finite subset of the BDM, dealing with those multisequences which are r-perfect. The largest eigenvalue λ of its transition matrix then yields the Hausdorff dimension of the set of r-perfect multisequences as

$$D_H = 1+ \frac{\log_q(\lambda)}{M}.$$

Also, we give a general formula for 1-perfect multisequences, for any M and q.

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References

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Author information

Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Austral de Chile, Casilla 567, Valdivia, Chile

    Michael Vielhaber & Mónica del Pilar Canales Ch.

Authors
  1. Michael Vielhaber
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  2. Mónica del Pilar Canales Ch.
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Guang Gong

  2. Department of Informatics, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

  3. Department of Electrical and Electronic Engineering, Yonsei University, 121-749, Seoul, Korea

    Hong-Yeop Song

  4. Dept. of Electronics and Electrical Engineering, Pohang University of Science and Technology (POSTECH), 790-784, Pohang, Kyungbuk, Korea

    Kyeongcheol Yang

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© 2006 Springer-Verlag Berlin Heidelberg

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Vielhaber, M., del Pilar Canales Ch., M. (2006). The Hausdorff Dimension of the Set of r-Perfect M-Multisequences. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_22

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  • DOI: https://doi.org/10.1007/11863854_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44523-4

  • Online ISBN: 978-3-540-44524-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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