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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 = pe (e ≥ 2)and period T = pe-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 /2 piis C a( τ ) = (-1 )k -1 T / p2i-1,where 1 ≤ k ≤ 2p i- 1,and gcd(k , 2p i ) = 1.This result shows there do exist some shifts such that the auto-correlations of l-sequences are high although most autocorrelations are low. Such result also holds for the decimations of l-sequences.
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 = pe (e ≥ 2) and period T = pe- 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 / 2 piis C a (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 auto-correlations of l-sequences are high although most autocorrelations are low. Such result also holds for the decimations of l-sequences.