On relationship between the parameters characterizing nonlinearity and nonhomomorphy of vector spaces transformation

We find a relation between the $W$-intersection matrix (which characterizes the degree of “nonhomomorphy”) of a transformation and the difference distribution table and the correlation matrix (which characterize the degree nonlinearity of a transformation). An upper estimate for the dimension of a subspace invariant under almost bent functions is put forward. A formula for evaluation of the $W$-intersection matrix of a composition of two transformations is obtained.