LFSR
Beginner
A small circuit that churns out a long string of random-looking test patterns.
Novice
Linear feedback shift register: a short chain of flip-flops whose input is the exclusive-OR of a few of its own bits. With the right feedback an -bit LFSR steps through all nonzero values in a fixed, random-looking order.
Expert
Described by a characteristic polynomial; a primitive polynomial gives maximum length. Used as the pattern generator in LBIST, as the expander in compression, and, with extra inputs, as a signature register. The all-zero state is stuck forever, so it must never be loaded.