Q-ary cascaded GMW sequences

Cascaded GMW sequences over GF(q) of arbitrary characteristic are investigated. Their periods are derived. As compared with the existing results on such sequences, substantially extended and improved theorems concerning their linear spans and autocorrelation functions are obtained. A criterion and an algorithm for constructing cascaded GMW sequences that have much larger linear spans than GMW sequences with the same periods are given. These provide a new class of complex-valued sequences which have larger linear spans and two-valued autocorrelation functions.