Research On The Correlation And Complexity Of Several Classes Of Pseudorandom Sequences

Pseudorandom sequences are widely used in communication systems and cryptog-raphy.Many randomness indexes have been proposed to measure the pseudo-random sequences,among which correlation,linear complexity and 2-adic complexity are three important indexes.For a single sequence,the autocorrelation function measures the difference between the sequence and its shift sequence.In radar,communication sys-tem and other related applications,the absolute value of the nontrivial autocorrelation function of the sequence is required to be as small as possible.In cryptography and other related applications,B-M algorithm and rational approximation algorithm show that the linear complexity and 2-adic complexity of the sequence should not be less than half of the period length.Therefore,the construction of sequences with good correlation properties,high linear complexity and 2-adic complexity are theoretical important and have a wide application background.In this thesis,we study the prop-erties and the constructions of the sequences with optimal correlation,high linear complexity and 2-adic complexity.The main work is as follows:1.The equivalence of quaternary sequences of even period with respect to the autocorrelation property and the unified forms of optimal quaternary sequences based on the cyclotomic classes of order 4 are defined in this paper.Then the unified forms of two classes of optimal quaternary sequences with respect to the autocorrelation property,which reveals the relationship between these two constructions,are given.Finally,the linear complexities over F₄of the optimal quaternary sequences with the known unified forms are determined.2.By using Hu's method,the 2-adic complexity of two kinds of binary sequences is studied.One is the Ding-Helleseth sequence,the other is the 4binary sequence constructed by Su et al.using the interleaving-technique.The results show that the2-adic complexity of these two kinds of sequences is larger than half of the period,which can resist the attack of rational approximation algorithm.3.By using the interleaving technique and the Gray inverse mapping,a class of quaternary sequences with period of 4is constructed,and the autocorrelation properties of the sequences are studied.The results show that the sequences have low autocorrelation properties.