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On the pseudorandomness of quaternary sequences derived from sequences over \(\mathbb F_4\)

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Abstract

In analogy to the corresponding measures of pseudorandomness for quaternary sequences introduced by Mauduit and Sárközy (for m-ary sequences) we introduce the well-distribution measure and correlation measure of order k for sequences over \(\mathbb F_4\). Using any fixed bijection from \(\mathbb F_4\) to the set of complex fourth roots of unity, we analyze the relation of these pseudorandomness measures for sequences over \(\mathbb F_4\) and for the corresponding quaternary sequences. More precisely, we show that they differ only by a multiplicative constant (depending only on k). We also apply the results for deriving new quaternary pseudorandom sequences from pseudorandom sequences over \(\mathbb F_4\) and vice versa.

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Acknowledgments

The first author thanks for the hospitality during his visit to RICAM, Austrian Academy of Science, and for the support by ÖAD Ernst-Mach follow-up scholarship. The second author is partially supported by the Austrian Science Fund FWF Project F5511-N26 which is part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”.

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Authors and Affiliations

  1. Department of Computer Science, Nankai University, Tianjin, 300071, People’s Republic of China

    Ming Su

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

    Arne Winterhof

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  1. Ming Su
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  2. Arne Winterhof
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Correspondence to Arne Winterhof.

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Su, M., Winterhof, A. On the pseudorandomness of quaternary sequences derived from sequences over \(\mathbb F_4\) . Period Math Hung 74, 79–87 (2017). https://doi.org/10.1007/s10998-016-0143-2

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  • DOI: https://doi.org/10.1007/s10998-016-0143-2

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