A Fibonacci-polynomial based coding method with error detection and correction

AbstractA Fibonacci coding method using Fibonacci polynomials is introduced. For integers m≥2, x≥1 and n≥1, an m×m matrix Qmn(x), the nth power of Qm(x), is considered as the encoding matrix, where Qm is an m×m matrix whose elements are Fibonacci polynomials. The decoding matrix Qm−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 large enough. Illustrative examples are provided