On the matrices of transitions of differences for some modular groups

Let $G_t$ be a translation group in a direct sum of groups $(Z/2^t,+)$. For the system of substitutions $G_rhG_s$ of order $2^n$ the matrices of digram transitions are investigated. A well-known hypothesis on the nonexistence of APN-substitutions of the field $GF(2^n)$ for even $n$ is partly verified. Some methods of construction of differentially $4$-uniform substitutions are suggested.