Matsumoto, Makoto; Kurita, Yoshiharu Twisted GFSR generators. (English) Zbl 0849.94014 ACM Trans. Model. Comput. Simul. 2, No. 3, 179-194 (1992). The authors propose a new pseudorandom number generator named the twisted generalized feedback shift register (TGFSR) generator and based on the linear recurrence \({\mathbf x}_{\ell+ n}:= {\mathbf x}_{\ell+ m} \oplus {\mathbf x}_\ell A\) \((\ell= 0, 1, \dots)\), where \({\mathbf x}_\ell\) is a word with components 0 or 1 of size \(w\) and is also regarded as a row vector over GF(2), \(A\) is a \(w\times w\) matrix over GF(2), and \(\oplus\) denotes the bitwise exclusive-or operation. This algorithm is a slightly but essentially modified version of the GFSR algorithm suggested by T. G. Lewis and W. H. Payne [J. ACM 20, 456-468 (1973; Zbl 0266.65009)]. The theoretical analysis and statistical tests given by the authors in this paper show that the TGFSR algorithm not only retains the well-known merits of the GFSR algorithm but also improves the original algorithm in many areas, and so the new generator is most suitable for simulation of a large distributive system, which requires a number of mutually independent pseudorandom number generators with compact size. Reviewer: Zhu Yaochen (Beijing) Cited in 2 ReviewsCited in 17 Documents MSC: 94A55 Shift register sequences and sequences over finite alphabets in information and communication theory 65C10 Random number generation in numerical analysis 11K45 Pseudo-random numbers; Monte Carlo methods Keywords:\(m\)-sequence; pseudorandom number generator; twisted generalized feedback shift register; GFSR algorithm; statistical tests; TGFSR algorithm Citations:Zbl 0849.94015; Zbl 0266.65009 PDFBibTeX XMLCite \textit{M. Matsumoto} and \textit{Y. Kurita}, ACM Trans. Model. Comput. Simul. 2, No. 3, 179--194 (1992; Zbl 0849.94014) Full Text: DOI Link Link