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In [K. Kuhapatanakul, The Lucas [Formula: see text]-matrix, Internat. J. Math. Ed. Sci. Tech. (2015), http://dx.doi.org/10.1080/0020739X.2015.1026612], Kuhapatanakul introduced Lucas [Formula: see text] matrix, [Formula: see text] whose elements are Lucas [Formula: see text] numbers. In this paper, we developed a new coding and decoding method followed from Lucas [Formula: see text] matrix, [Formula: see text]. We established the relations among the code matrix elements, error detection and correction for this coding theory. Correction ability of this method is [Formula: see text]% for [Formula: see text] and for [Formula: see text], the correction ability is [Formula: see text]%. In general, correction ability of this method increases as [Formula: see text] increases.

In this paper, we develop hybrid matrix cryptography followed by Fibonacci Qp,h(x) matrix, where h(x) is a polynomial with real coefficients and p = 1, 2, 3, …. They are the generalization of classical Fibonacci Q matrix for a continuous domain. They are used for designing super reliable cryptosystems.