Lower Bounds on Sequence Complexity Via Generalised Vandermonde Determinants

  • Nicholas Kolokotronis
  • Konstantinos Limniotis
  • Nicholas Kalouptsidis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4086)


Binary sequences generated by nonlinearly filtering maximal length sequences with period 2 n –1 are studied in this paper. We focus on the particular class of equidistant filters and provide improved lower bounds on the linear complexity of the filtered sequences. This is achieved by first considering and proving properties of generalised Vandermonde determinants. Furthermore, it is shown that the methodology developed can be used for studying properties of any nonlinear filter.


Binary sequences filter functions linear complexity linear feedbak shift registers symmetric functions Vandermonde determinants 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nicholas Kolokotronis
    • 1
  • Konstantinos Limniotis
    • 1
  • Nicholas Kalouptsidis
    • 1
  1. 1.Department of Informatics and TelecommunicationsNational and Kapodistrian University of AthensAthensGreece

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