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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The $ k$-dimensional distribution of combined GFSR sequences


Author: Shu Tezuka
Journal: Math. Comp. 62 (1994), 809-817
MSC: Primary 65C10; Secondary 94A55
MathSciNet review: 1223233
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Abstract: We develop an efficient method for analysis of the k-dimensional distribution of combinations of several GFSR sequences by bitwise exclusive-or operations. First, we introduce the notion of a resolution-wise lattice structure for GFSR sequences, and show that by applying a theorem of Couture to this type of lattice, we obtain a precise description of k-dimensional distribution of combined GFSR sequences in the same way as for combined Tausworthe sequences. Finally, we apply this method to the combination of two different Twisted GFSR generators, which were recently proposed by Matsumoto and Kurita, and investigate the order of equidistribution of the combined sequence.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1223233-9
PII: S 0025-5718(1994)1223233-9
Keywords: GFSR sequences, Twisted GFSR, k-dimensional distribution, lattice structure
Article copyright: © Copyright 1994 American Mathematical Society