State Diagrams of a Class of Singular LFSR and Their Applications to the Construction of de Bruijn Cycles

TL;DR

This paper analyzes the unique state diagrams of a class of singular LFSRs and introduces an algorithm to construct de Bruijn cycles from these diagrams, expanding methods for sequence generation.

Contribution

It presents a detailed analysis of singular LFSR state diagrams and proposes a novel algorithm for constructing de Bruijn cycles from them.

Findings

State diagrams of the class of singular LFSR have special structures

An algorithm for constructing de Bruijn cycles from these diagrams is developed

The approach broadens the methods for sequence and cycle construction

Abstract

The state diagrams of a class of singular linear feedback shift registers (LFSR) are discussed. It is shown that the state diagrams of the given LFSR have special structures. An algorithm is presented to construct a new class of de Bruijn cycles from the state diagrams of these singular LFSR.