A Fibonacci coding method is introduced using Extended Generalized Fibonacci Polynomials in this paper. A new square matrix Qⁿm (a, b), the nᵗʰ power of Qm(a, b) of order m × m is defined whose elements are based on extended Generalized Fibonacci Polynomial. Matrix Qⁿ m (a, b) for integer x ≥ 1, a ≥ 1 and b ≥ 1 is considered as the encoding matrix and a matrix Q−ⁿm (a, b) is considered as decoding matrix. An error-detection and error-correction method is also defined in Extended Generalized Fibonacci polynomials.
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