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.
Keywords
Fibonacci number
Mathematics
Separable space
Secret sharing
Finite field
Fibonacci polynomials
Discrete mathematics
Combinatorics
Cryptography
Difference polynomials
Algorithm
Orthogonal polynomials
Subject Areas
Coding theory and cryptography
·Artificial Intelligence ·Physical Sciences
Cryptographic Implementations and Security
·Artificial Intelligence ·Physical Sciences
Cellular Automata and Applications
·Computational Theory and Mathematics ·Physical Sciences
Citations by Year
2017: 3
2021: 1
2025: 2
Loading…
Loading…