The third order variations on the Fibonacci universal code

Abstract

In this paper, we have studied the third order variations on the Fibonacci universal code and we have displayed tables GH(3) a (n) we have defined for −20 ≤ a ≤ −2 and 1 ≤ n ≤ 100. Also, we have compared with the third order variations on the Fibonacci universal code and the second order variations on the Fibonacci universal code[2] in terms of cryptography and we have found that the third order variations on the Fibonacci universal code is more advantageous than the second order variations on the Fibonacci universal code.

Gopala-Hemachandra codes revisited

“…Moreover, it appears that there exists at most k consecutive integers for which GH 3 −(10+k) code does not exist. Both of these observations are true in the limited range for which tables are constructed in [8]. It would be nice to prove these two statements.…”

“…The third order Gopala-Hemachandra codes GH 3 a are defined using the recurrence relation GH a codes for −20 ≤ a ≤ −2 and 1 ≤ n ≤ 100. However, [8] is a computationally oriented paper and does not have general results. It appears that GH 3 a codes are universal for −10 ≤ a ≤ −2.…”

“…[n] = GH[n − 1] + GH[n − 2] + GH[n − 3], for n ≥ 4 and the initial conditions GH[1] = a, GH[2] = 1 − a and GH[3] = 1.In[8], Nalli and Ozyilmaz determined tables of GH3 …”

Bivariate Variations of Fibonacci and Narayana Sequences and Universal Codes

“…Moreover, cryptographic applications can be made using these codes or representations. There are many works on these codes in literature (see for example [5][6][7][8][9][10]).…”

Some New Codes on the k – Fibonacci Sequence

“…e Fibonacci Q p -matrices were introduced (see [9]), and in [10], for p � 1, a coding theory is obtained on the Fibonacci Q p -matrices. Also, a Fibonacci coding method is introduced by using Fibonacci polynomials and Fibonacci sequence (see [8,[11][12][13][14]). Here, we introduce some coding methods on k-Fibonacci sequence.…”