基于广义欧拉商二元序列线性复杂度研究

Linear complexity of binary sequences derived from generalized Euler quotients

文章给出了广义欧拉商的定义,讨论了广义欧拉商的若干性质,并利用广义欧拉商构造一类伪随机二元序列,通过线性递推关系确定了序列p(奇素数)模4情况下的线性复杂度大于周期的1/2,尤其在p(奇素数)模4余3的情形下,线性复杂度仅仅比周期少1。

In this paper,the definition of generalized Euler quotient is given,and some properties of generalized Euler quotient are discussed.A class of pseudorandom binary sequences is constructed by using generalized Euler quotients.The linear complexity of the sequences,in the case of odd prime p≡1 or 3(mod 4),is more than half of the period;especially,in the case of p≡3(mod 4),the linear complexity is only 1 less than the period.