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On the Periods of Generalized Fibonacci Recurrences
, 1992
"... We give a simple condition for a linear recurrence (mod 2 w ) of degree r to have the maximal possible period 2 w 1 (2 r 1). It follows that the period is maximal in the cases of interest for pseudorandom number generation, i.e. for 3term linear recurrences dened by trinomials which are prim ..."
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Cited by 35 (11 self)
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We give a simple condition for a linear recurrence (mod 2 w ) of degree r to have the maximal possible period 2 w 1 (2 r 1). It follows that the period is maximal in the cases of interest for pseudorandom number generation, i.e. for 3term linear recurrences dened by trinomials which are primitive (mod 2) and of degree r > 2. We consider the enumeration of certain exceptional polynomials which do not give maximal period, and list all such polynomials of degree less than 15. 1.
Uniform Random Number Generators for Supercomputers
 Proc. Fifth Australian Supercomputer Conference
, 1992
"... We consider the requirements for uniform pseudorandom number generators on modern vector and parallel supercomputers, consider the pros and cons of various classes of methods, and outline what is currently available. We propose a class of random number generators which have good statistical propert ..."
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Cited by 35 (14 self)
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We consider the requirements for uniform pseudorandom number generators on modern vector and parallel supercomputers, consider the pros and cons of various classes of methods, and outline what is currently available. We propose a class of random number generators which have good statistical properties and can be implemented efficiently on vector processors and parallel machines. A good method for initialization of these generators is described, and an implementation on a Fujitsu VP 2200/10 vector processor is discussed. 1
Uniform Random Number Generators for Vector and Parallel Computers
 REVISION APPEARED IN PROC. FIFTH AUSTRALIAN SUPERCOMPUTER CONFERENCE
, 1992
"... We consider the requirements for uniform pseudorandom number generators on modern vector and parallel machines; consider the pros and cons of various popular classes of methods and some new methods; and outline what is currently available. We then make a proposal for a class of random number gen ..."
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Cited by 8 (1 self)
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We consider the requirements for uniform pseudorandom number generators on modern vector and parallel machines; consider the pros and cons of various popular classes of methods and some new methods; and outline what is currently available. We then make a proposal for a class of random number generators which have good statistical properties and can be implemented efficiently on vector processors and parallel machines. A proposal regarding initialization of these generators is made. We also discuss the results of a trial implementation on a Fujitsu VP 2200/10 vector processor.
Chaotic Sequences of I.I.D. Binary Random Variables with Their Applications to Communications
"... Abstract: The Bernoulli shift is a fundamental theoretic model of a sequence of independent and identically distributed(i.i.d.) binary random variables in probability theory, ergodic theory, information theory, and so on. We give a simple sufficient condition for a class of ergodic maps with some sy ..."
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Abstract: The Bernoulli shift is a fundamental theoretic model of a sequence of independent and identically distributed(i.i.d.) binary random variables in probability theory, ergodic theory, information theory, and so on. We give a simple sufficient condition for a class of ergodic maps with some symmetric properties to produce a chaotic sequence of i.i.d. binary random variables. This condition is expressed in terms of binary function, which is a generalized version of the Rademacher function for the dyadic map. Applications of such a sequene to communications are also discussed briefly 1