Research On The Linear Complexities Of Several Classes Of Quaternary Sequences

Pseudo-random sequences are widely used in coding,cryptography,code di-vision multiple access(CDMA)communication systems,radar,sonar and and so on.In the application related to cryptography,the pseudo-random sequences are required to have high linear complexity.Due to their nice algebraic structures,cy-clotomic sequences have received a lot of attentions in recent years.In the thesis,we will study the linear complexities of two classes of quaternary generalized cyclotomic sequences over F4 and Z4,respectively.1.Based on generalized cyclotomic modulo 2pm,a new kind of quaternary gener-alized cyclotomic series with period of 2pm is constructed.We study the linear complexities of this kind of sequences over F4 and Z4,respectively.It is proved that this class of sequence has high linear complexity.2.Based on generalized cyclotomic modulo 2pmqn,a new kind of quaternion gen-eralized cyclotomic series with period of 2pmqn is constructed.We study the linear complexity of this kind of sequences on F4.It is proved that this classes of sequence has high linear complexity.