A study on linear pseudorandom number generators with long period

研究了有限域上基于线性递归的伪随机数生成器。伪随机数是蒙特卡罗模拟中不可缺少的工具。仿真中经常使用线性伪随机数生成器。在本研究中，我们研究了线性伪随机数发生器在权分布检验中的性质。研究了发生器的递推形式与其初始状态的关系。在权值分布检验中，我们还分析了递归形式与它们的输出之间的关系。构造了具有极大等分布性质的伪随机数生成器。

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.