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On the number of multiples of certain primitive polynomials over GF(2)

On the number of multiples of certain primitive polynomials over GF(2) Introduction Pseudorandom numbers are vitally important for Monte Carlo methods, and many recent computer simulation programs need millions, or sometimes, billions of pseudorandom numbers. One of famous generator of pseudorandom numbers which can produce a long period sequence is m- sequence. Lindholm [] studied Hamming weights of long sequences of msequences and gave the moments of Hammming weights by their characteristic polynomials. Jordan-Wood [2] gave a formula for the distribution of Hamming weights of m-sequences. Moreover, Kurita [4] tested statistically m-sequences with characteristic: trinomials, and revealed statistical biases of such m-sequences with respect to Hamming weights. In many computer programms of Monte Carlo method, pseudorandom numbers are used to simulate (discrete or discretized) stochastic processes. Thus, it is very important to know whether the pseudorandom number generators used in the programs can make good imitations of the stochastic processes under consideration. For this purpose. Takashima [12] introduced a statisticaltest for pseudorandom numbers based on sojourn times of 1-dimensional random walk and reported that m-sequences with characteristic primitive trinomials showr graphical gaps in simulations of sojourn times. Graphs of simulations of sojourn times by m-sequences generated by the method of Fushimi [1] also present present explicit gaps. His method http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monte Carlo Methods and Applications de Gruyter

On the number of multiples of certain primitive polynomials over GF(2)

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References (6)

Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0929-9629
eISSN
1569-3961
DOI
10.1515/mcma.1996.2.1.15
Publisher site
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Abstract

Introduction Pseudorandom numbers are vitally important for Monte Carlo methods, and many recent computer simulation programs need millions, or sometimes, billions of pseudorandom numbers. One of famous generator of pseudorandom numbers which can produce a long period sequence is m- sequence. Lindholm [] studied Hamming weights of long sequences of msequences and gave the moments of Hammming weights by their characteristic polynomials. Jordan-Wood [2] gave a formula for the distribution of Hamming weights of m-sequences. Moreover, Kurita [4] tested statistically m-sequences with characteristic: trinomials, and revealed statistical biases of such m-sequences with respect to Hamming weights. In many computer programms of Monte Carlo method, pseudorandom numbers are used to simulate (discrete or discretized) stochastic processes. Thus, it is very important to know whether the pseudorandom number generators used in the programs can make good imitations of the stochastic processes under consideration. For this purpose. Takashima [12] introduced a statisticaltest for pseudorandom numbers based on sojourn times of 1-dimensional random walk and reported that m-sequences with characteristic primitive trinomials showr graphical gaps in simulations of sojourn times. Graphs of simulations of sojourn times by m-sequences generated by the method of Fushimi [1] also present present explicit gaps. His method

Journal

Monte Carlo Methods and Applications – de Gruyter

Published: Jan 1, 1996

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