Research And Application Of Two New Types Of Sequences And Sequence Sets

Pseudo-random sequences are widely used in spread spectrum communication system,secret communication,pseudo-random code ranging,delay measurement,signal synchronization and radar navigation currently.The main indicators that measure randomness properties of a sequence are period,correlation properties,linear complexity and 2-adic complexity and so on.In this paper,we study a class of sequence sets with good correlation and its application,and calculate the 2-adic complexity of another class of a generalized cyclotomic sequence.Good correlation property is one of the theoretical guarantees of pseudo-random sequences in practical applications.Compared with the perfect complementary sequence sets,quasi-complementary sequence set(QCSSs)with good correlation properties have the large advantage in a multicarrier CDMA communication,because it can support more users communicate at the same time.According to the approach of constructing periodic QCSSs by Zilong Liu et al,a kind of new periodic QCSS is proposed in this paper based on an almost different set and the existing optimal quaternary sequence set.Then,we find the proposed QCSS is near-optimal by calculating the period tolerance of the quasi-complementary sequence set(maximum correlation value).Meanwhile,with the changes of the values of parameters in the QCSS,the number of users supported by the subcarrier channels in CDMA system has an exponential growth.Stream ciphers require that the 2-adic complexity of a key stream sequence must be greater than half of the sequence period to resist attacks by the rational approximation algorithms(RAA).In this paper,the 2-adic complexity of a class of binary Ding-Helleseth generalized cyclotomic sequence with order 2 based on twin prime numbers is obtained by calculating the Gaussian periods of the sequence.The results show that the 2-adic complexity of the sequence can be optimal,ie.the 2-adic complexity is equal to the period.