The generalized relations among the code elements for Fibonacci coding theory

A Fibonacci-polynomial based coding method with error detection and correction

“…The approach presented is considered a Fibonacci-polynomial based coding method. Obviously, this is an extension of the results in [12] based on the Q n p matrices. By substituting a positive integer for x, an infinite number of matrices of order m ≥ 2 are obtained.…”

“…Parts of the p-Fibonacci sequences for p = 1, 2, 3, 4 are listed in the table below. The p-Fibonacci sequences have been used to construct coding and decoding matrices [12][13][14]. The Q p matrix of order p + 1 is introduced in [12].…”

“…The p-Fibonacci sequences have been used to construct coding and decoding matrices [12][13][14]. The Q p matrix of order p + 1 is introduced in [12]. For 0 ≤ p ≤ 3, the matrix Q p is given below.…”

“…For 0 ≤ p ≤ 3, the matrix Q p is given below. It is shown in [12] that for n ≥ 1 and p ≥ 0, the nth power of Q p , denoted Q n p , is…”

“…These matrices have been used in [12] to give a coding and decoding technique referred to as Fibonacci coding theory.…”