Randomly-Flipped Linear Feedback Shift Registers: Spectral Analysis and Conjectures

We introduce a general framework for characterizing the power spectrum of antipodal processes with finite memory m and exploit it to analyze the behavior of and LFSR in which the linear combination of the states is randomly flipped before being fed back into the register. The spectra reveal noteworthy regularities that can be explored by means of the proposed theory and give raise to some conjectures.