Long range variations on the Fibonacci universal code

Abstract: Fibonacci coding is based on Fibonacci numbers and was defined by Apostolico and Fraenkel (1987) . Fibonacci numbers are generated by the recurrence relation with initial terms , . 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 . We have found that there is no Gopala–Hemachandra code for a particular positive integer n and for a particular value of . We conclude that for , Gopala–Hemachandra code exists for . Also, for , there is at most m consecutive not available (N/A) Gopala–Hemachandra code in column where . And, for , as m increases the availability of Gopala–Hemachandra code decreases in column where . [Copyright &y& Elsevier]