Improvement of pseudorandom number generators from viewpoint of algebra and statistics

(1)我们提出了统计检验的自适应修正，特别是TestU01。此过程会自动增加样本量，并再次测试PRNG。当p值下降到一个明显可拒绝的范围时，它就停止了。(2)我们用C和c++语言实现了MT19937和WELL19937的跳转代码。这些都是从一个主页上分发的。(3)本文提出了一种利用MacWilliams恒等式计算若干prng的第2位到第6位的权值分布的方法。

(1) We proposes an adaptive modification of statistical tests, in particular TestU01. This procedure automatically increases the sample size, and tests the PRNG again. It stops when the p-value falls in a clearly rejectable range. (2) We have implemented the codes of the jumping-ahead for MT19937 and WELL19937, in C and C++ languages. These are distributed from a homepage. (3) we report a method to compute the weight distribution of the second to the sixth lowest bits of several PRNGs by using MacWilliams identity.