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

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.