A NOTE ON LINEAR CODES WITH GENERALIZED FIBONACCI MATRICES
By
Munesh Kumari1, Kalika Parasd1* and Jagmohan Tanti2
1Department of Mathematics, Central University of Jharkhand-835205, Ranchi, India
2Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, Uttar Pradesh, India
Email: muneshnasir94@gmail.com, jagmohan.t@gmail.com
*Corresponding author: Email: klkaprsd@gmail.com
(Received: August 10, 2022; Revised: September 25, 2022; Accepted: September 30, 2022)
DOI: https://doi.org/10.58250/jnanabha.2022.52209
Abstract
In this paper, we investigate the linear codes from generalized Fibonacci matrices in the context of coding theory. We show that Fibonacci matrices form a generator matrix for the first order ReedMuller codes R(1, 1). Further, we see that Multinacci matrices form a basis for [n, n, 1] MDS-code.
2020 Mathematical Sciences Classification: 11B39, 11T71, 94B05.
Keywords and Phrases: Basis, Coding Theory, Fibonacci Matrix, Linear code, LCD code