The Moore-Penrose Inverse of the Rectangular Fibonacci Matrix and Applications to the Cryptology

In this paper, we define the general form of the Moore-Penrose inverse for the matrix whose elements are Fibonacci numbers. We examine the states of the matrix F ∈ Mm, n(C), where F is a rectangular Fibonacci matrix based on the values of m and n. In the second part of this study, we introduce a novel coding theory using the MoorePenrose inverse of the rectangular Fibonacci matrix and provide illustrative examples. The rectangular Fibonacci matrix plays a crucial role in the construction of the coding algorithm. This coding method is referred to as the "coding theory on rectangular Fibonacci matrix." Received: August 12, 2023Accepted: October 19, 2023