A New Coding Theory on Fibonacci n-Step Polynomials

Abstract

In this paper, we develop a new series of Fibonacci \ud835\udc5b-step polynomials. Based on these series of polynomials, we introduce a new class of square matrix of order \ud835\udc5b. Thereby, we define a new coding theory called \u00a0Fibonacci \ud835\udc8f-step \u00a0polynomials \u00a0coding \u00a0theory. \u00a0Then \u00a0we \u00a0calculate \u00a0the \u00a0generalized \u00a0relations \u00a0among \u00a0the code \u00a0elements \u00a0for \u00a0all \u00a0values \u00a0of \ud835\udc5b. \u00a0It \u00a0is \u00a0shown \u00a0that, \u00a0for \ud835\udc5b = 2, the \u00a0correct \u00a0ability \u00a0of \u00a0this \u00a0method \u00a0is 93.33% whereas for n \u00a0= \u00a03, 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 \ud835\udc65 and increases as \ud835\udc5b increases.