关于渐近随机的GFSR序列的设计

Ｔｏｏｔｉｌｌ等人提出了一种渐近的随机Ｔａｕｓｗｏｒｔｈｅ序列，并给出了一个偶然发现的此种序列，但直到现在尚未有人提出一个寻求此种序列的系统性的方法，本文中我们将给出一种设计ＧＦＳＲ序 算法，所产生的序列近似地满足渐近随机性，我们的算法基于反复地运用由Ｆｕｓｈｉｍｉ提出的算法，由现在的算法所设计出来的序列不有一种附加的好处，即其十中抽一的序列也是近似地渐近随机的，文中给出了一些数字例子。

Designing Asymptotically Random GFSR Sequences

Tootill et al. Proposed the concept of an asymptotically random Tausworthe sequence, and gave an example of such sequence found by chance. However, no systematic way of finding such sequences has been proposed by now. In this paper we will give an algorithm for designing GFSR sequences which satisfy the asymptotic randomness approximately. Our algorithm is based on repeated applications of the algorithm proposed by Fushimi. The sequences designed by the present algorithm have an added merit that their decimated sequences are also approximately asymptotically random. Some numerical examples will be shown.