k-order Gaussian Fibonacci polynomials and applications to the coding/decoding theory

In this paper we define k-order Gaussian Fibonacci polynomials with boundary conditions and give the generating function, explicit formula and some identities for k-order Gaussian Fibonacci polynomials. We introduce the matrix represent and we obtain the k-order Gaussian Fibonacci Polynomials matrix...

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Bibliographic Details
Published in:	Journal of discrete mathematical sciences & cryptography Vol. 25; no. 5; pp. 1399 - 1416
Main Authors:	Asci, Mustafa, Aydinyuz, Suleyman
Format:	Journal Article
Language:	English
Published:	Taylor & Francis 04.07.2022
Subjects:	Coding/decoding method Fibonacci numbers Fibonacci polynomials Gaussian Fibonacci numbers k-order Gaussian Fibonacci numbers k-order Gaussian Fibonacci polynomial coding/decoding theory k-order Gaussian Fibonacci Polynomials
ISSN:	0972-0529, 2169-0065
Online Access:	Get full text
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Summary:	In this paper we define k-order Gaussian Fibonacci polynomials with boundary conditions and give the generating function, explicit formula and some identities for k-order Gaussian Fibonacci polynomials. We introduce the matrix represent and we obtain the k-order Gaussian Fibonacci Polynomials matrix. We define a new coding theory called k-order Gaussian Fibonacci Polynomials coding theory and establish the code elements for values of k. This coding/decoding method bound to the Q k (x), R k (x) and E k,n (x) matrices. So, this method is different from the classical algebraic coding. Consequently, with this method, we move the coding theory onto a complex space which is a different field. Therefore, new working areas are created.
ISSN:	0972-0529 2169-0065
DOI:	10.1080/09720529.2020.1816917