Code matrix is the matrix of which on element and its neighbors are arranged to have a code value. The code matrix was originally designed by the author for developing a vision system but has not been theoretically studied. In this paper some theoretical properties of the code matrix are investigated. The studied characteristics of the code matrix are useful for not only understanding the matrix itself but efficiently restructuring the matrix. A number of transformation functions, which enable the matrix to have different shape, are thus developed based on the investigated properties. The transformation functions are then applied to build a perfectly and uniformly structured square code matrix, which is proven useful in on image processing example. The study in this paper is expected to serve a theoretical background for the application of the code matrix in many areas.