Optimal Codes from Fibonacci Polynomials and Secret Sharing Schemes

TL;DR

This paper investigates cyclic codes generated by Fibonacci polynomials over finite fields, demonstrating their potential to produce optimal codes with applications in secret sharing schemes.

Contribution

It introduces a novel class of cyclic codes from Fibonacci polynomials and explores their optimality and applications in secret sharing.

Findings

Most codes are maximum distance separable and optimal

Examples illustrating the code properties are provided

Applications to secret sharing schemes are demonstrated

Abstract

In this work, we study cyclic codes that have generators as Fibonacci polynomials over finite fields. We show that these cyclic codes in most cases produce families of maximum distance separable and optimal codes with interesting properties. We explore these relations and present some examples. Also, we present applications of these codes to secret sharing schemes.