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
Several new bounds for the correlation functions of de Bruijn sequences are derived.It is shown that the set of all primitive de Bruijn sequences have the following two properties:1)for each sequence a in the set with...Several new bounds for the correlation functions of de Bruijn sequences are derived.It is shown that the set of all primitive de Bruijn sequences have the following two properties:1)for each sequence a in the set with large span n,the magnitude of its auto-correlation funct-ion|r<sub>a</sub>（k）|is relatively small compared with the peak 2<sup>n</sup> for all k≠0 mod 2<sup>n</sup>;2)for each pair of sequences a,b in the set with large span n,the magnitude of their cross-correlation function |r<sub>ab</sub>（k）| is relatively small compared with the peak 2<sup>n</sup> for all k.Some generalizations of the result are also presented.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 （?）.
基金Projects supported by National Natural Science Foundation of China
文摘Several new bounds for the correlation functions of de Bruijn sequences are derived.It is shown that the set of all primitive de Bruijn sequences have the following two properties:1)for each sequence a in the set with large span n,the magnitude of its auto-correlation funct-ion|r<sub>a</sub>（k）|is relatively small compared with the peak 2<sup>n</sup> for all k≠0 mod 2<sup>n</sup>;2)for each pair of sequences a,b in the set with large span n,the magnitude of their cross-correlation function |r<sub>ab</sub>（k）| is relatively small compared with the peak 2<sup>n</sup> for all k.Some generalizations of the result are also presented.
