Correlation Of Binary Sequences

Pseudorandom sequences with optimal autocorrelation and low cross correlation was widely used in radar distance, hardware testing, code-division multiple-access (CDMA) communication systems and cryptology, etc.. In CDMA communication sys-tems, the sequence are applied to acquire accurate timing information and success-fully combat interference from the other users who share a common channel. On the other hand, the sequences employed in either stream cipher encryptions as key stream generators or in digital signature algorithms as pseudorandom number generators can effectively resist cross correlation attacks.In chapter3of this paper, using the balance property of twin prime sequence and its interleaved structure, we proved a binary sequences u=A(a, e)+b of period N=4p(p+2) with almost balance property and four valued autocorrelation, ie., Cu(τ)∈{N,0,±4} for any τ, where α=(0,1,1,1) and b is a twin prime sequence of period p(p+2). At the same time, the complete autocorrelation distribution and the exact linear complexity under some premise of the sequence u were mathematically given. In chapter4, we derived the cross correlation value of three families of ADS sequences, constructed by three pairs of binary sequences as based sequences of ADS sequence. The fist pair is a generalized GMW sequence of period N=22k-1and its modified version, the second pair is a pair of Legendre sequences of period N=p(p odd prime) with their respective fist terms complementary, the third is a twin prime sequence of period N=p(p+2) and its modified version.