%0 Journal Article %T A new Gaussian Fibonacci matrices and its applications %J Journal of Algebra and Related Topics %I University of Guilan %Z 2345-3931 %A Prasad, B. %D 2019 %\ 06/01/2019 %V 7 %N 1 %P 65-72 %! A new Gaussian Fibonacci matrices and its applications %K Gaussian Fibonacci numbers %K Fibonacci numbers %K Golden mean %R 10.22124/jart.2019.12999.1144 %X In this paper, we introduced a new Gaussian Fibonacci matrix, $G^{n}$ whose elements are Gaussian Fibonacci numbers and we developed a new coding and decoding method followed from this Gaussian Fibonacci matrix, $G^{n}$. We established the relations between the code matrix elements, error detection and correction for this coding theory. Correction ability of this method is $93.33$\%. %U https://jart.guilan.ac.ir/article_3721_49da7f8b20ac8534782e530a53b0cea1.pdf