Long range variations on the Fibonacci universal code

The third order variations on the Fibonacci universal code

“…For n = 1, 2, ..., 100 the representation or not available (N/A) of GH codes for a ≤ −2 are displayed for m = 2, M.Basu and B.Prasad concluded [2]. In this paper , we study for values of n the Zeckendorf's representation doesn't available for a ≤ −2 .…”

“…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.…”

“…The family of GH codes GH (m) a , which satisfy our condition for encoding all of the desirable integers 1 ≤ n ≤ M (where M is the number of possible source message), allow us to have many more universal codes at our disposal when transmitting a message [2].…”

“…Since we will be using this correspondence in several examples , let's record it for future use : Then we will obtain GH code of the number corresponding to every letter in text message from table3 (if m = 3 ) or table2 in [2] (if m = 2). Later we will add '0' (s) to the end of GH codes of the numbers such that the length of GH code of every number in text message is equal to the length of the longest GH code in text message .…”

“…The representation will be unique if one uses the following procedure to produce it: given the integer B, find the largest Fibonacci number F (2) r smaller or equal to B; then continue recursively with B − F (2) r . For example 16 = 3 + 13, so its binary Fibonacci representation would be 001001.…”