中文摘要：

当在 GF (p) 上看作了序列时，几个几何序列有很低的线性复杂性，例如时期 qn 的二进制序列吗？1 由禅宗和比赛构造了[12 ](q 是主要力量下午， p 是一个奇怪的素数) 与最大的可能的线性复杂性 qn 吗？1 当在 GF (2 ) 上看作了序列时。这显示那二进制代码与线性复杂性 LC2 和线性复杂性人员登陆艇不是的低 GF (p) 在流零为使用固定的高 GF (2 ) 定序。在这篇文章，二进制序列的线性复杂性被证明的 GF (p) 和结果上的几更低的界限被用于 GF (p) Blum-Blum-Shub 的线性复杂性，自我缩小，并且 de Bruijn 序列。二进制代码的数字上的更低的界限与 LC2 定序 > 人员登陆艇也被介绍。

英文摘要：

Several geometric sequences have very low linear complexities when considered as sequences over GF（p）, such as the binary sequences of period q^n - 1 constructed by Chan and Games [1-2] （q is a prime power p^m, p is an odd prime） with the maximal possible linear complexity q^n-1 when considered as sequences over GF（2）. This indicates that binary sequences with high GF（2） linear complexities LC2 and low GF（p）-linear complexities LCp are not secure for use in stream ciphers. In this article, several lower bounds on the GF（p）-linear complexities of binary sequences is proved and the results are applied to the GF（p）-linear complexities of Blum-Blum-Shub, self-shrinking, and de Bruijn sequences. A lower bound on the number of the binary sequences with LC2 〉 LCD is also presented.