Right Circulant Matrices with Generalized Fibonacci and\ Lucas Polynomials and Coding Theory

TL;DR

This paper introduces new coding algorithms based on right circulant matrices constructed from generalized Fibonacci and Lucas polynomials, exploring their properties and applications in coding theory.

Contribution

It presents novel coding algorithms utilizing right circulant matrices with generalized Fibonacci and Lucas polynomials, expanding the mathematical tools in coding theory.

Findings

Developed two new coding algorithms using circulant matrices

Analyzed properties of matrices with generalized Fibonacci and Lucas polynomials

Demonstrated potential applications in coding theory

Abstract

In this paper, we give two new coding algorithms by means of right circulant matrices with elements generalized Fibonacci and Lucas polynomials. For this purpose, we study basic properties of right circulant matrices using generalized Fibonacci polynomials $F_{p,q,n}\left( x\right) $, generalized Lucas polynomials $L_{p,q,n}\left( x\right) $ and geometric sequences.