Let \underline{S}=(S,S,…) be a binary random sequence with period N=2~n, where S=(S_0,…,S_(N-1)) 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(\underline{S})=2-(2N+1)2~(-N)-2~(-2N);2)E|c(\underline{S})-c(\underline{S}+\underline{b})|=[2~(c(\underline{b})+1)-2]2~(-N)for any sequence \underline{b} with period 2~n;3)N-1+2~(-N)-(n/2+1-2~(-(N-n)))≤E[$$mi{n}_{W(b)\le 1}$$c(\underline{S}+\underline{b})]≤N-1+2~(-N)4)2-2~(-(N-1))≤E[\[min_{W(b)\le 1}\|c(\underline{S})-c(\underline{S}+\underline{b})|]≤2-2~(-N)+n/2-2~(-(N-n)), where E and Var stand for taking expectation and variance respectively, c(\underline{b}) is the linearcomplexity of the sequence \underline{b} and W(b) the Hamming weight of one period of the seqnence \underline{b}.

Let \underline{S}=(S,S,…) be a binary random sequence with period N=2~n, where S=(S_0,…,S_(N-1)) 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(\underline{S})=2-(2N+1)2~(-N)-2~(-2N);2)E|c(\underline{S})-c(\underline{S}+\underline{b})|=[2~(c(\underline{b})+1)-2]2~(-N)for any sequence \underline{b} with period 2~n;3)N-1+2~(-N)-(n/2+1-2~(-(N-n)))≤E[$$mi{n}_{W(b)\le 1}$$c(\underline{S}+\underline{b})]≤N-1+2~(-N)4)2-2~(-(N-1))≤E[\[min_{W(b)\le 1}\|c(\underline{S})-c(\underline{S}+\underline{b})|]≤2-2~(-N)+n/2-2~(-(N-n)), where E and Var stand for taking expectation and variance respectively, c(\underline{b}) is the linearcomplexity of the sequence \underline{b} and W(b) the Hamming weight of one period of the seqnence \underline{b}.