Study On Design And Randomness Analysis Of Pseudorandom Sequences

Pseudorandom sequences have wide applications in ranging systems,spread-spectrum conmunication systems,code division multiple-access systems,software testing systems, radar systems and stream ciphers.This dissertation investigate the construction and randomness analysis of some kinds of generalized cyclotomic sequences and a low-correlation zone sequence sets.The author obtains main results as follows:(1) Based on Ding and Helleseth's generalized cyclotomy,new generalized cyclotomic sequences of order two and length pq have been constructed.Two methods have been used to calculate the autocorrelation values of these sequences.In one of them the theory of cyclotomic number is used.In the other,the same result is concluded by redefining the sequences using Legendre symbol.(2) The linear complexity of the sequences in(1) has been determined.The result shows that the minimum is((p+1)(q-1))/2,the maximum is pq-1,and the sequences are good from the linear complexity viewpoint.(3) Based on Ding and Helleseth's generalized cyclotomy,the generalized cyclotonfic sequences of order four and length pq have been constructed.The sequences are the generalization of the sequences in(1).And the linear complexity of the sequences has been deterrmined.(4) Based on the Ding generalized cyclotomy,new generalized cyclotomic sequences of order 2^k and length pq have been constructed by finding out a special characteristic set.The linear complexity of the sequences has been determined.The minimum is (pq-1)/2 and the maxinmm is pq.(5) Based on Whiteman's generalized cyclotomy,new generalized cyclotomic sequences of order two and length pq have been constructed and the lower bound of the linear complexity of these sequences has been determined.(6) The constructions and the randomness properties of all kinds of Ding's generalized cyclotomic sequences and Whiteman's generalized cyclotomic sequences were summarized. The definitions of both the sequences are redefined by Legendre symbol, based on which the reason has been derived that Whiteman's generalized eyclotomic sequences are better than Ding's generalized cyclotomic sequences.(7) A column sequence set of period 3^m+1-1 has been devised by the idea of confusion and balance from the ternary sequences of period 3^m-1 with ideal autocorrelation property proposed by Helleseth et al,and new ternary low correlation zone sequence sets of period 3ⁿ-1 have been constructed by using the column sequence set,where m and n are different positive integers with(m+1)|n.With respect to Tang-Fan-Matsufuji bound,the low correlation zone sequence sets are optimal.