扩展在上GF(3)新型自缩序列模型及研究  

New model and studying of self-shrinking sequence developed on GF(3)

作　　者：王锦玲[1] 陈亚华[1] 兰娟丽[1] 

机构地区：[1]郑州大学数学系,郑州450001

出　　处：《计算机工程与应用》2009年第35期114-119,共6页Computer Engineering and Applications

基　　金：河南省教育厅自然科学指导性项目NO.200510459003~~

摘　　要：自收缩序列是一类重要的伪随机序列,而周期和线性复杂度是序列伪随机性的经典量度。如何构造自缩序列的新模型,使生成序列具有大的周期和高的线性复杂度是一个重要的问题。针对这一问题,构造了GF(3)上一种新型的自缩序列模型,利用有限域理论,研究了生成序列的周期和线性复杂度,得到一些主要结论:周期上界3n,下界32骔n/3」;线性复杂度上界3n,下界32骔n/3」-1。进一步讨论了基于GF(3)上本原三项式和四项式的自缩序列的周期和线性复杂度。Self-shrinking sequence is an important kind of pseudo-random sequences.Period and linear complexity are classic measures of pseudo-random sequences.So,it becomes an important issue to construct new models of self-shrinking sequence that could generate sequences with great period and high linear complexity.In view of this question,a new model of self-shrinking sequence over GF（3） is constructed.After the study of the period and linear complexity of the generated sequence using the theory of finite fields,there are some main conclusions：The upper bound of the period is 3^n ,the lower bound is 3^2[n/3];The upper bound of linear complexity is 3^n ,the lower bound is 3^2[n/3]-2 .Moreover,the period and linear complexity of the generated sequence based on primitive trinomials and quarternomials of degree n over GF（3） are discussed.

关 键 词：自缩序列 周期 线性复杂度 本原三项式 本原四项式 

分 类 号：TN918.4[电子电信—通信与信息系统]