Continued fraction for formal laurent series and the lattice structure of sequences

Besides equidistribution properties and statistical independence the lattice profile, a generalized version of Marsaglia's lattice test, provides another quality measure for pseudorandom sequences over a (finite) field. It turned out that the lattice profile is closely related with the linear complexity profile. In this article we give a survey of several features of the linear complexity profile and the lattice profile, and we utilize relationships to completely describe the lattice profile of a sequence over a finite field in terms of the continued fraction expansion of its generating function. Finally we describe and construct sequences with a certain lattice profile, and introduce a further complexity measure

Counting functions and expected values for the lattice profile at n

10.1016/j.ffa.2004.01.004Finite Fields and their Applications104636-65