A Fibonacci-polynomial based coding method with error detection and correction
A Fibonacci coding method using Fibonacci polynomials is introduced. For integers m?2 m ? 2 , x?1 x ? 1 and n?1 n ? 1 , an mm m  m matrix Q m n ( x ) , the n n th power of Qm(x) Q m ( x ) , is considered as the encoding matrix, where Qm Q m is an mm m  m matrix whose elements are Fibonacci polynomials. The decoding matrix Q m ? n ( x ) is also introduced. A simple error-detecting criterion and a simple error-correcting method for this class of codes are given. It is shown that the probability of decoding error is almost zero for m m large enough. Illustrative examples are provided.
fibonacci polynomial fibonacci-polynomial matrices error detecting and error correcting codes