Generalization of GMW sequences and No sequences

GMW sequences and families of No sequences are generalized. Generalized GMW sequences have ideal autocorrelation and balance properties and generalized No sequences also have optimal correlation properties in terms of Welch's lower bound. The linear spans of the generalized GMW and No sequences appear to be large although there is not at present a closed-form expression for the linear span. A count of the numbers of cyclically distinct generalized GMW sequences and generalized No sequences that can be constructed is provided. Generalized GMW sequences have also been found in the literature by Klapper et al. (1993) under the name "cascaded GMW sequences".