AN EXTENDED GENERALIZED FIBONACCI POLYNOMIAL BASED CODING METHOD WITH ERROR DETECTION AND CORRECTION
By
Vaishali Billore¹∗, Naresh Patel² and Hemant Makwana³
¹Department of Applied Mathematics, Institute of Engineering & Technology, Indore, Madhya Pradesh, India-452001
²Department of Applied Mathematics, Government Holkar (Model, Autonomous) Science College, Indore, Madhya Pradesh, India-452001
³Department of Information & Technology, Institute of Engineering & Technology, Indore, Madhya Pradesh, India-452001
Email: ∗vaishali.billore20@gmail.com, n_patel_1978@yahoo.co.in, hmakwana@ierdavv.edu.in (Here ∗ is the corresponding author)
(Received: March 15, 2023; In format: March 24, 2023; Revised April 13, 2023; Accepted April 24, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53127
Abstract
A Fibonacci coding method is introduced using Extended Generalized Fibonacci Polynomials in this paper. A new square matrix Qⁿm (a, b), the nᵗʰ power of Qm(a, b) of order m × m is defined whose elements are based on extended Generalized Fibonacci Polynomial. Matrix Qⁿ m (a, b) for integer x ≥ 1, a ≥ 1 and b ≥ 1 is considered as the encoding matrix and a matrix Q−ⁿm (a, b) is considered as decoding matrix. An error-detection and error-correction method is also defined in Extended Generalized Fibonacci polynomials.
2020 Mathematical Sciences Classification: 11C08, 11C20, 11H71.
Keywords and Phrases: Extended Generalized Fibonacci Polynomial, Extended Generalized Fibonacci Polynomial matrices, Error detection and Error correction.