The Cycle Structure of LFSR with Arbitrary Characteristic Polynomial over Finite Fields

TL;DR

This paper characterizes the cycle structure of LFSRs with any monic polynomial over finite fields, providing methods to identify states and new representations for each cycle.

Contribution

It introduces a comprehensive analysis of LFSR cycle structures with arbitrary characteristic polynomials and proposes novel methods for state identification and representation.

Findings

Complete cycle structure characterization for LFSRs over finite fields

New methods for finding states in each cycle

Innovative state representation techniques

Abstract

We determine the cycle structure of linear feedback shift register with arbitrary monic characteristic polynomial over any finite field. For each cycle, a method to find a state and a new way to represent the state are proposed.