Linear difference equations and periodic sequences over finite fields

TL;DR

This paper investigates linear difference equations and periodic sequences over finite fields, exploring their properties and connections with de Bruijn graphs to enhance understanding of their structure and applications.

Contribution

It provides new insights into linear equations and periodic sequences over finite fields, linking them with de Bruijn graphs for the first time.

Findings

Characterization of solutions to linear difference equations over finite fields

Analysis of periodic sequences and their properties

Connection established between periodic sequences and de Bruijn graphs

Abstract

First, we study the linear equations in general. Second, we focus our attention in periodic sequences over finite fields and de Bruijn directed graph.