In this paper, the autocorrelations of maximal period Feedback with Carry Shift Register sequences （l-sequences） are discussed. For an l-sequence a with connection integer q = p^e（e ≥ 2） and period T = p^t-1（p- ...In this paper, the autocorrelations of maximal period Feedback with Carry Shift Register sequences （l-sequences） are discussed. For an l-sequence a with connection integer q = p^e（e ≥ 2） and period T = p^t-1（p- 1）, and for any integer i, 1 ≤ i ≤ e/2, by calculating the number of certain sets, it is shown that the autocorrelation of a with shift τ= kT/2p^i is Ca（τ） =（-1）^k-1 T/p^2i-1, where 1 ≤ k ≤ 2p^i - 1, and gcd（k,2p^i） = 1. This result shows there do exist some shifts such that the autocorrelations of l-sequences are high although most autocorrelations are low. Such result also holds for the decimations of l-sequences.展开更多
基金This work was supported in part by a grant from the Major State Basic Research Development Program of China （973 Program） （No. 2007CB311201）, and the National Science Foundation of China （No. 60473029, No.60673072）.
基金the 863 Project of China (No.2006AA01Z417) the National Natural Science Foundation of China (No.60673081).
文摘In this paper, the autocorrelations of maximal period Feedback with Carry Shift Register sequences （l-sequences） are discussed. For an l-sequence a with connection integer q = p^e（e ≥ 2） and period T = p^t-1（p- 1）, and for any integer i, 1 ≤ i ≤ e/2, by calculating the number of certain sets, it is shown that the autocorrelation of a with shift τ= kT/2p^i is Ca（τ） =（-1）^k-1 T/p^2i-1, where 1 ≤ k ≤ 2p^i - 1, and gcd（k,2p^i） = 1. This result shows there do exist some shifts such that the autocorrelations of l-sequences are high although most autocorrelations are low. Such result also holds for the decimations of l-sequences.
