m序列完备递归采样值的存在条件

Existence Condition of the Complete Recurrence Sampling Values of m-Sequences

本文用群论方法讨论了n级m序列完备递归采样值的存在条件,证明了对任意n级m序列,其完备递归采样值存在的充要条件是商群G=Z_p~*/H(其中p=2~n—1,Z_p~*={s|(s,p)=1},H={1,2,2~2,…,2^(n-1))为循环群。在完备递归采样值存在的条件下,求出了完备递归采样值的个数为n.φ(φ(2~n—1)/n)。最后给出了递归采样值的一个重要性质。

We discuss the existence condition for the complete recurrence sampling value of msequences. It is proved that for m-sequences of order n, the sufficient and necessary conditions that the complete recurrence sampling value exists are that the quotient group G=Z_p~*/H(p= 2~n-1,Z_p~*={s|(s,p)=1},H=l,2~2,2~3,…,2~n-1}) is cylcic group, and that the number of the complete recurrence sampling values is n·φ(φ(2~n-1)/n). In the end, we give some important characteristics of the complete recurrence sampling of m-sequences.