Also we propose the method,by replacing the GMW sequence required in constructing PC sequence with the cascaded GMW sequences,thus can improve the properties of the PC sequence.

Using cascade GMW sequences and shift sequences of the inner sequences,cascade unified sequences can be quickly constructed.

GMW sequences over Galois rings and their linear complexities;

The PC sequence with length of (2~n-1)~2 can be generated by interleaving the GMW sequence with length of 2~n-1 and interleaved sequence with length of (2~n-1)~2.

A new family of GMW sequences over an arbitrary Galois ring with the characteristic of p~2 is constructed,which generalizes the related result of Udaya and Siddiqi for the case that the Galois ring is Z_4.

Trinomial properties of three families of nonlinear spreading sequences (GMW sequences, No sequences and Kasami sequences) are discussed in this paper.

In this paper, a new algorithm to construct GMW sequences and cascaded GMW sequences by shift sequences is proposed.

This paper gives the necessary and sufficient conditions when the two GMW sequences have the same generator polynomials, and discussed the further conclusions.

It is verified that the GMW PC sequences have balance,optimal auto/cross correlation functions,and very large linear spans and can be used in the CDMA spread spectrum communication and cryptography.