Masanori Fushimi

The k -distribution of generalized feedback shift register pseudorandom numbers

A necessary and sufficient condition is established for the generalized feedback shift register (GFSR) sequence introduced by Lewis and Payne to be k-distributed. Based upon the theorem, a theoretical test for k-distributivity is proposed and performed in a reasonable amount of computer time, even for k = 16 and a high degree of resolution (for which statistical tests are impossible because of the astronomical amount of computer time required). For the special class of GFSR generators considered by Arvillias and Maritsas based on the primitive trinomial Dp + Dq + 1 with q = an integral power of 2, it is shown that the sequence is k-distributed if and only if the lengths of all subregisters are at least k. The theorem also leads to a simple and efficient method of initializing the GFSR generator so that the sequence to be generated is k-distributed.

Random number generation with the recursion X t =X t-3p ⊕X t-3q

Abstract A generalized feedback shift register (GFSR) algorithm proposed by Lewis and Payne (1973) uses a primitive trinomial to generate a sequence of pseudorandom numbers. We propose a similar algorithm which uses a primitive polynomial with many nonzero terms, but generates a number as fast as the original GFSR algorithm. Our sequence is guaranteed to be equidistributed in higher dimensions and to have a good autocorrelation property. Extensive statistical tests have been performed on the sequences generated by our algorithm and the results were quite satisfactory.

Designing a uniform random number generator whose subsequences are k -distributed

A method for designing a uniform random number generator based on M-sequence is described. It generates a k-distributed sequence

An equivalence relation between Tausworthe and GFSR sequences and applications

\{ x_t ;t = 0,1,2, \cdots \}

Calculation of fibonacci polynomials for gfsr sequences with low discrepancies

such that its decimated sequences

Random Number Generation On Parallel Processors

\{ x_{nt} ;t = 0,1,2, \cdots \}

The Efficiency Analysis of Skyscrapers Based on the Inner Traffic

are also k-distributed for several values of n. The sequence is obtained by permuting the bits in Tausworthe sequence; a suitable permutation is found by solving a special

Fast generation of low discrepancy points based on Fibonacci polynomials

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The efficient shape of a skyscraper based on the vertical traffic

integer linear programme, a set covering problem. The constraint matrix of the programme is obtained by applying a modified Gaussian elimination to another

Increasing the orders of equidistribution of the leading bits of the Tausworthe sequence

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