2010 Fiscal Year Final Research Report

A study on linear pseudorandom number generators with long period

Research Project

Project/Area Number	20740050
Research Category	Grant-in-Aid for Young Scientists (B)
Allocation Type	Single-year Grants
Research Field	General mathematics (including Probability theory/Statistical mathematics)
Research Institution	Yamagata University
Principal Investigator	NISHIMURA Takuji Yamagata University, 理学部, 准教授 (90333947)
Project Period (FY)	2008 – 2010
Keywords	擬似乱数生成法 / 重み分布 / 初期値
Research Abstract	We studied pseudorandom number generators based on linear recurrences over finite fields. Pseudorandom numbers are indispensable tools for Monte Carlo simulations. Linear pseudorandom number generators are often used in the simulations. In this research, we studied properties of linear pseudorandom number generators in the weight distribution tests. Relationship between the form of the recurrence of generators and their initial states are studied. We analyzed also relationship between the form of the recurrence and their outputs in the weight distribution tests. We constructed pseudorandom number generators with maximally equidistribution property.