GMW Sequences over Galois Rings with Large Linear Complexities and Optimal Correlation

A new family of GMW sequences over an arbitrary Galois ring with the characteristic of p2 is constructed, which generalizes the related result of Udaya and Siddiqi for the case that the Galois ring is Z4. Such GMW sequences have large period and optimal correlation in terms of Welch′s lower bound. Utilizing the discrete Fourier transform, both the upper and lower bounds on the linear complexities of this family of GMW sequences are investigated. The result shows that such sequences have large linear complexities.