【摘要】 密码学意义上强的序列不仅应该具有足够高的线性复杂度,而且当少量比特发生改变时不会引起线性复杂度的急剧下降,即具有高的k^-错复杂度。该文以多项式的因式分解为主要工具研究了任意有限域GF（q）上,周期N与p互素以及N=p^v这两种情况下,计数函数N_N,O（C）的值,井给出了线性复杂度的数学期望E_N,O的值以及k^-错复杂度的数学期望E_N,k的一个有用的下界,这里p是有限域GF（q）的特征。更多还原

【Abstract】 Cryptographically strong sequences not only should have a large linear complexity, but also no a significant decrease of the linear complexity when a few terms are changed. This requirement leads to the concept of the k-error linear complexity of periodic sequences. In the following two cases: （1） gcd（N,p） =1; （2） N =p^v,where p denotes the characteristic of the finite field GF（q）, the counting function N_N,o（c）,i.e., the number of N-periodic sequences with given linear complexity c, is showed, the expected value of the linear complexity E_N,o is determined, and a useful lower bound on the expected value of the κ-error linear complexity E_N,k is established.更多还原