A Criterion for Determining the Crosscorrelation of Binary Sequences from GMW Constructions

A binary sequence from the GMW constructions is defined by a chain of power functions and trace functions. In this paper, for such a sequence, we present a criterion on the decimation such that the crosscorrelation between its decimation and its adjoint sequence is independent of all the powers. Since a binary GMW or cascaded GMW sequence is the same as its adjoint sequence, the crosscorrelation of the sequence and its decimations can be determined from known results on m-sequences by the criterion. Furthermore, we discuss the 3-valued and 4-valued correlation functions of cascaded GMW sequences.