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International Conference on Sequences and Their Applications

SETA 2006: Sequences and Their Applications – SETA 2006 pp 47–60Cite as

On the Linear Complexity of Sidel’nikov Sequences over \({\mathbb {F}}_d\)

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

Abstract

We study the linear complexity of sequences over the prime field \({\mathbb{F}_d}\) introduced by Sidel’nikov. For several classes of period length we can show that these sequences have a large linear complexity. For the ternary case we present exact results on the linear complexity using well known results on cyclotomic numbers. Moreover, we prove a general lower bound on the linear complexity profile for all of these sequences. The obtained results extend known results on the binary case. Finally we present an upper bound on the aperiodic autocorrelation.

The first author has been supported by the Austrian Science Fund (FWF) grant S83 and by the Austrian Academy of Sciences.

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Author information

Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040, Linz, Austria

    Nina Brandstätter

  2. Sabanci University, Orhanli, Tuzla, Istanbul, 34956, Turkey

    Wilfried Meidl

Authors
  1. Nina Brandstätter
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  2. Wilfried Meidl
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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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Brandstätter, N., Meidl, W. (2006). On the Linear Complexity of Sidel’nikov Sequences over \({\mathbb {F}}_d\) . 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_5

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  • DOI: https://doi.org/10.1007/11863854_5

  • 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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