Study Of Some Topics On The Linear Complexities Of Pseudorandom Sequence

Pseudo-random-sequences have a wide application in coding,cryptography,code division multiple access(CDMA)communication systems,radar,sonar and and so on.In stream chiper,pseudorandom sequences can be used as keys.In this cases,the pseudo-random sequence should have a high linear complexity to guarantee that the sequence is sufficiently unpredictable and random.In this thesis,we will focus on some topics of the linear complexities of pseudo-random sequences.we will determine the linear complexity(LC)over the general finite field of quaternary sequences with period 2p derived from binary Legendre sequences and quaternary sequences with period 2p(p+ 2)derived from twin-prime sequences pair,respectively.And,we will consider the k-error linear complexity of a new binary generalized cyclotomic sequence of period p2.Our main results are summarized as follows.1.Using the discrete Fourier transform over the finite field,we determine the linear complexity over the general finite field of the quaternary sequence constructed from the Legendre sequence.2.Using the discrete Fourier transform over the finite field,we determine the linear complexity over the general finite field of the quaternary sequence constructed from the two-prime sequences.3.Using the Fermat quotients,we study the k-error linear complexity of a class of new generalized cyclotomic binary sequence.