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The Ramanujan Journal

, Volume 25, Issue 2, pp 155–178 | Cite as

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

  • Katalin Gyarmati
  • Christian Mauduit
  • András Sárközy
Article

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 (for every fixed ) and the symmetry measures are small. Finally, the symmetry measures are estimated for truly random binary lattices.

Keywords

Binary lattice Pseudorandom Symmetry 

Mathematics Subject Classification (2000)

11K45 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Katalin Gyarmati
    • 1
  • Christian Mauduit
    • 2
  • András Sárközy
    • 1
  1. 1.Department of Algebra and Number TheoryEötvös Loránd UniversityBudapestHungary
  2. 2.Institut de Mathématiques de LuminyCNRS, UMR 6206Marseille Cedex 9France

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