【作者】 陈亚华；

【导师】 王锦玲；

【作者基本信息】 郑州大学 ， 基础数学， 2009， 硕士

【摘要】 自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问题.本文构造了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,得到了如下结论:周期上界为3ⁿ,下界为3^?;线性复杂度上界为3ⁿ,下界为3^?;并讨论了基于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.且进一步把此模型推广到了任意的有限域GF（q）,得到的生成序列的周期上界为（?）,下界为q^?;线性复杂度上界为（?）,下界为q^?.且当q=2时,恰是文献[1]中的结果.更多还原

【Abstract】 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 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 3ⁿ, the lower bound is 3^{2（?）n/3（?）} ;The upper bound of linear complexity is 3ⁿ, the lower bound is 3^{2（?）n/3（?）-1} ; Moreover, the period and linear complexity of the generated sequence based on primitive trinomials and quarternomials of degree n over are discussed. And the model is extended to arbitrary finite field GF（q）. Obtain these conclusions :the upper bound of the period of the generated sequences is （qⁿ（q-1））/2 the lower bound is q^{（q-1）（?）n/q（?）}; The upper bound of linear complexity of the generated sequences is （qⁿ（q-1））/2 , the lower bound is q^{（q-1）（?）n/q（?）-1}更多还原