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Fibonacci shift operation on Fibonacci numbers of order m

Prasad B.

Control and Cybernetics

2016

Vol. 45, no. 2

259--266

Fibonacci codes of diﬀerent orders are of variable length. They are used for encoding of numbers and ﬁnd applications in information and coding theory. The Fibonacci binary encoding and computation of its values are closely associated with Fibonacci shift operations. Walder et al. (2012) established a relation for kth Fibonacci left shift for Fibonacci numbers of order m = 2,3. In this paper, we establish a relation for kth Fibonacci left shift for Fibonacci numbers of order m = 4 and we generalize the formula for kth Fibonacci left shift for the Fibonacci numbers of all orders.