NDLI: Lattice structure of pseudorandom sequences from shift-register generators

Content Provider	IEEE Xplore Digital Library
Author	Tezuka, S.
Copyright Year	1990
Description	Author affiliation: IBM Res., Tokyo, Japan (Tezuka, S.)
Abstract	The author develops a theory of the lattice structure of pseudorandom sequences from shift register generators, i.e. Tausworthe sequences and GFSR (generalized feedback shift register) sequences. The author defines an analog of linear congruential sequences in GF(2,x), the field of all Laurent series over the Galois field of two elements GF(2), and shows that this class of sequences contains as a subclass the Tausworthe sequence. He derives a theorem that links the k-distribution of such sequences and the successive minima of the k-dimensional lattice over GF(2,x) associated with the sequences, thereby leading to the geometric interpretation of the lattice structure in the k-dimensional unit space of these sequences. This result is generalized to define the successive minima for the point set of k-dimensional vectors each consisting of k consecutive terms of GFSR sequences, and it is shown that GFSR sequences have a similar structure to that of Tausworthe sequences. A simulation problem in which shift-register-type pseudorandom sequences yield useless results due to such lattice structures is discussed.
Starting Page	266
Ending Page	269
File Size	289738
Page Count	4
File Format	PDF
ISBN	0911801723
DOI	10.1109/WSC.1990.129525
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1990-12-09
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Lattices Random sequences Shift registers Polynomials Feedback Galois fields Laboratories Computational modeling Ear Random number generation
Content Type	Text
Resource Type	Article

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