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

This work addresses a problem in combinatorics and coding theory for researchers in discrete mathematics and cryptography, but it appears incremental as it builds on existing LFSR theory.

The paper tackles the problem of constructing de Bruijn cycles by analyzing state diagrams of a specific class of singular linear feedback shift registers (LFSR), showing they have special structures and presenting an algorithm to generate a new class of de Bruijn cycles from these diagrams.