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

Katalin Gyarmati (1) , Christian Mauduit (2) , András Sárközy (1)

1 Department of Algebra and Number Theory [Budapest]
2 IML - Institut de mathématiques de Luminy

InanearlierpaperGyarmatiintroducedandstudiedthesymmetrymeasure 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.

Mots clés: Binary lattice; Pseudorandom; Symmetry

Domaines: Théorie des nombres [math.NT]

Katalin Gyarmati, Christian Mauduit, András Sárközy. Measures of pseudorandomness of finite binary lattices, II. (The symmetry measures). Ramanujan Journal, 2011, 25 (2), pp.155-178. ⟨10.1007/s11139-010-9255-0⟩. ⟨hal-01272279⟩