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Boolean Functions Derived from Pseudorandom Binary Sequences

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Sequences and Their Applications – SETA 2012 (SETA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7280))

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Abstract

We study measures used to assess Boolean functions, where the functions are understood to be derived from binary sequences. We prove relations between two complexity measures for these Boolean functions and the correlation measure of order k of the corresponding sequence. More precisely, we study sparsity and combinatorial complexity of the Boolean function. Moreover, for a sequence with ’typical’ values of the correlation measure of order k we apply these relations to derive bounds on the complexity measures for the corresponding Boolean function. Finally, we apply our results to Sidelnikov sequences for which nice upper bounds on the correlation measure are known.

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Author information

Authors and Affiliations

  1. Institute for Financial Mathematics, Kepler University Linz, Altenbergerstr. 69, A-4040, Linz, Austria

    Gottlieb Pirsic

  2. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Str. 69, A-4040, Linz, Austria

    Arne Winterhof

Authors
  1. Gottlieb Pirsic
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  2. Arne Winterhof
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, P.O. Box 7803, 5020, Bergen, Norway

    Tor Helleseth

  2. Department of Mathematics, Simon Fraser University, 8888 University Drive, V5A 1S6, Burnaby, BC, Canada

    Jonathan Jedwab

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Pirsic, G., Winterhof, A. (2012). Boolean Functions Derived from Pseudorandom Binary Sequences. In: Helleseth, T., Jedwab, J. (eds) Sequences and Their Applications – SETA 2012. SETA 2012. Lecture Notes in Computer Science, vol 7280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30615-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-30615-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30614-3

  • Online ISBN: 978-3-642-30615-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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