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A complexity measure for families of binary sequences

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Abstract

In earlier papers finite pseudorandom binary sequences were studied, quantitative measures of pseudorandomness of them were introduced and studied, and large families of “good” pseudorandom sequences were constructed. In certain applications (cryptography) it is not enough to know that a family of “good” pseudorandom binary sequences is large, it is a more important property if it has a “rich”, “complex” structure. Correspondingly, the notion of “f-complexity” of a family of binary sequences is introduced. It is shown that the family of “good” pseudorandom binary sequences constructed earlier is also of high f-complexity. Finally, the cardinality of the smallest family achieving a prescibed f-complexity and multiplicity is estimated.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501, Bielefeld, Germany E-mail

    Rudolf Ahlswede & Levon H. Khachatrian

  2. Institut de Mathématiques de Luminy, CNRS–UPR 9016, 163 Avenue de Luminy, Case 907, F-13288, Marseille Cedex 9, France

    C. Mauduit

  3. Department of Algebra and Number Theory, Eötvös Loránd University, H-1117, Budapest, Pázmány Péter sétány 1/c, Hungary E-mail

    A. Sárközy

Authors
  1. Rudolf Ahlswede
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  2. Levon H. Khachatrian
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  3. C. Mauduit
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  4. A. Sárközy
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Ahlswede, R., Khachatrian, L.H., Mauduit, C. et al. A complexity measure for families of binary sequences. Periodica Mathematica Hungarica 46, 107–118 (2003). https://doi.org/10.1023/A:1025962825241

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  • DOI: https://doi.org/10.1023/A:1025962825241

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