On primary functions which are minimally close to linear functions

The investigation of aspects of closeness to linear functions for functions from $(\mathbf Z/(p))^n$ to $(\mathbf Z/(p))^m$ ($p$ is prime number). New criteria of minimal closeness to linear functions are found. This property of a function is proved to be inherited for its homomorphic images. As a generalization of an analogous statement for Boolean functions it is proved that if $p=2$ or $3$ then a class of functions which are minimally close to linear ones coincides with the class of bent-functions (if bent-functions do exist).