On the complexity of decoding Boolean cube splitting into cube faces

We consider the known problem of decoding functions of Boolean algebra, that is, we need to completely restore the table of values of a function defined on an $n$-dimensional Boolean cube $B^n$ using its values on some subset of $B^n$. If the function belongs to some narrower class than the class of all functions of $n$ variables (for example, to the set of monotone or threshold functions), then only vectors of a subset of $n$-dimensional Boolean cube can be required to completely determine the function. In the paper, we consider the class of functions which split the $n$-dimensional Boolean cube into cube faces. An asymptotic estimate for complexity of decoding functions that belong to any subclass of this class with fixed structure is obtained.