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

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Abstract

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.

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  1. Sabanci University, Orhanli, Tuzla, 34956, Istanbul, Turkey

    Wilfried Meidl

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  1. Wilfried Meidl
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Correspondence to Wilfried Meidl.

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Meidl, W. Continued fraction for formal laurent series and the lattice structure of sequences. AAECC 17, 29–39 (2006). https://doi.org/10.1007/s00200-006-0195-2

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  • DOI: https://doi.org/10.1007/s00200-006-0195-2

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