Let （?）=（S,S,…）be a binary random sequence with period N=2<sup>n</sup>,where S=(S<sub>0</sub>,…,S<sub>N-1</sub>)is its one period with N independent and uniformly distributed ...Let （?）=（S,S,…）be a binary random sequence with period N=2<sup>n</sup>,where S=(S<sub>0</sub>,…,S<sub>N-1</sub>)is its one period with N independent and uniformly distributed binary random variables.The main results of this paper are as follows.1)Var c（?）=2-（2N+1）2<sup>-N</sup>-2<sup>-2N</sup>;2)E|c（?）-c（?）|=[2<sup>c（?）+1</sup>-2]2<sup>-N</sup>for any sequence （?） with period 2<sup>n</sup>;3)N-1+2<sup>-N</sup>-(n/2+1-2<sup>-（N-n）</sup>)≤E[（?）c（?）]≤N-1+2<sup>-N</sup>4)2-2<sup>-（N-1）</sup>≤E[（?）|c（?）-c（?）|]≤2-2<sup>-N</sup>+n/2-2<sup>-（N-n）</sup>,where E and Var stand for taking expectation and variance respectively,c（?） is the linearcomplexity of the sequence （?） and W（b） the Hamming weight of one period of the seqnence （?）.展开更多
基金This project was supported by National Natural Science Foundation of China
文摘Let （?）=（S,S,…）be a binary random sequence with period N=2<sup>n</sup>,where S=(S<sub>0</sub>,…,S<sub>N-1</sub>)is its one period with N independent and uniformly distributed binary random variables.The main results of this paper are as follows.1)Var c（?）=2-（2N+1）2<sup>-N</sup>-2<sup>-2N</sup>;2)E|c（?）-c（?）|=[2<sup>c（?）+1</sup>-2]2<sup>-N</sup>for any sequence （?） with period 2<sup>n</sup>;3)N-1+2<sup>-N</sup>-(n/2+1-2<sup>-（N-n）</sup>)≤E[（?）c（?）]≤N-1+2<sup>-N</sup>4)2-2<sup>-（N-1）</sup>≤E[（?）|c（?）-c（?）|]≤2-2<sup>-N</sup>+n/2-2<sup>-（N-n）</sup>,where E and Var stand for taking expectation and variance respectively,c（?） is the linearcomplexity of the sequence （?） and W（b） the Hamming weight of one period of the seqnence （?）.
