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On the pseudorandomness of binary and quaternary sequences linked by the gray mapping

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Abstract

Binary and quaternary sequences are the most important sequences in view of many practical applications. Any quaternary sequence can be decomposed into two binary sequences and any two binary sequences can be combined into a quaternary sequence using the Gray mapping. We analyze the relation between the measures of pseudorandomness for the two binary sequences and the measures for the corresponding quaternary sequences, which were both introduced by Mauduit and Sárközy. Our results show that each ‘pseudorandom’ quaternary sequence corresponds to two ‘pseudorandom’ binary sequences which are ‘uncorrelated’.

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Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics, Altenberger Straße 69, A-4040, Linz, Austria

    Radwa Marzouk

  2. Department of Mathematics, Faculty of Science Cairo University, Giza, Egypt

    Radwa Marzouk & Arne Winterhof

Authors
  1. Radwa Marzouk
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  2. Arne Winterhof
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Correspondence to Radwa Marzouk.

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Communicated by András Sárközy

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Marzouk, R., Winterhof, A. On the pseudorandomness of binary and quaternary sequences linked by the gray mapping. Period Math Hung 60, 13–23 (2010). https://doi.org/10.1007/s10998-010-1013-y

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  • DOI: https://doi.org/10.1007/s10998-010-1013-y

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