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

  • Nina Brandstätter
  • Wilfried Meidl
Conference paper

DOI: 10.1007/11863854_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4086)
Cite this paper as:
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

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.

Keywords

Sidel’nikov sequence Linear complexity Linear complexity profile Aperiodic autocorrelation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nina Brandstätter
    • 1
  • Wilfried Meidl
    • 2
  1. 1.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  2. 2.Sabanci UniversityOrhanli, Tuzla, IstanbulTurkey

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