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Measures of pseudorandomness of finite binary lattices, II. (The symmetry measures)

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Abstract

In an earlier paper Gyarmati introduced and studied the symmetry measure of pseudorandomness of binary sequences. The goal of this paper is to extend this definition to two dimensions, i.e., to binary lattices. Three different definitions are proposed to do this extension. The connection between these definitions is analyzed. It is shown that these new symmetry measures are independent of the other measures of pseudorandomness of binary lattices. A binary lattice is constructed for which both the pseudorandom measures of order ℓ (for every fixed ℓ) and the symmetry measures are small. Finally, the symmetry measures are estimated for truly random binary lattices.

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Authors and Affiliations

  1. Department of Algebra and Number Theory, Eötvös Loránd University, 1117, Budapest, Pázmány Péter sétány 1/C, Hungary

    Katalin Gyarmati & András Sárközy

  2. Institut de Mathématiques de Luminy, CNRS, UMR 6206, 163 avenue de Luminy, Case 907, 13288, Marseille Cedex 9, France

    Christian Mauduit

Authors
  1. Katalin Gyarmati
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  2. Christian Mauduit
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  3. András Sárközy
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Corresponding author

Correspondence to Katalin Gyarmati.

Additional information

Research partially supported by Hungarian National Foundation for Scientific Research, Grants Nos. K67676, K72731 and PD72264, French–Hungarian exchange program F-48/06, and the János Bolyai Research Fellowship.

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Gyarmati, K., Mauduit, C. & Sárközy, A. Measures of pseudorandomness of finite binary lattices, II. (The symmetry measures). Ramanujan J 25, 155–178 (2011). https://doi.org/10.1007/s11139-010-9255-0

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  • DOI: https://doi.org/10.1007/s11139-010-9255-0

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