TY - JOUR
T1 - A New Coding Theory on Fibonacci n-Step Polynomials
AU - Monojit Das and Manjusri Basu
JO - Journal of Information and Computing Science
VL - 1
SP - 056
EP - 073
PY - 2024
DA - 2024/01
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22464.html
KW -  Fibonacci  numbers,  Fibonacci  n-step  numbers,  Fibonacci  polynomials,  Fibonacci  n-step 
polynomials, Fibonacci n-step polynomials coding, Error correction. 

AB - In this paper, we develop a new series of Fibonacci ?-step polynomials. Based on these series of 
polynomials, we introduce a new class of square matrix of order ?. Thereby, we define a new coding theory 
called  Fibonacci ?-step  polynomials  coding  theory.  Then  we  calculate  the  generalized  relations  among  the 
code  elements  for  all  values  of ?.  It  is  shown  that,  for ? = 2, the  correct  ability  of  this  method  is 93.33% 
whereas for n  =  3, the correct ability of this method is 99.80%. The interesting part of this coding/decoding 
method is that the correct ability does not depend on ? and increases as ? increases.