Long range variations on the Fibonacci universal code

Fibonacci coding is based on Fibonacci numbers and was defined by Apostolico and Fraenkel (1987) [1], . Fibonacci numbers are generated by the recurrence relation Fi=Fi−1+Fi−2 ∀i⩾2 with initial terms F0=1, F1=1. Variations on the Fibonacci coding are used in source coding as well as in cryptography. In this paper, we have extended the table given by Thomas [8]. We have found that there is no Gopala–Hemachandra code for a particular positive integer n and for a particular value of a∈Z. We conclude that for n=1,2,3,4, Gopala–Hemachandra code exists for a=−2,−3,…,−20. Also, for 1⩽n⩽100, there is at most m consecutive not available (N/A) Gopala–Hemachandra code in GH−(4+m) column where 1⩽m⩽16. And, for 1⩽n⩽100, as m increases the availability of Gopala–Hemachandra code decreases in GH−(4+m) column where 1⩽m⩽16.