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


DOI: 10.1007/s00200-006-0195-2

Cite this article as:
Meidl, W. AAECC (2006) 17: 29. doi:10.1007/s00200-006-0195-2


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.


Sequences over finite fieldsContinued fraction expansionMarsaglia's lattice testLinear complexity

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Sabanci UniversityIstanbulTurkey