Some New Fibonacci Matrices and Error Detecting-Correcting Codes

The rapid and accurate transfer of information is essential in today’s digital world, where error detecting and correcting codes play a crucial role. In this context, Fibonacci numbers have been extensively applied in coding theory, particularly in coding structures based on Fibonacci polynomials and symmetric matrices. This study proposes a novel coding framework by defining and using some new Fibonacci matrices with their determinants. The properties of these matrices are analyzed to construct efficient coding and error correction mechanisms. The proposed structure enables the transmission of larger data volumes in a single iteration without compromising the error correction performance, demonstrating the potential of Fibonacci matrices for reliable and efficient information transfer.