  Under study are eigenfunctions of $q$-ary $n$-dimensional hypercube. Given
all values of an eigenfunction in the sphere we develop methods to reconstruct
the function in full or in part. First, we obtain that all values of the
function in the corresponding ball are uniquely determined under some
supplementary conditions. Secondly, if the radius is equal to the eigenvalue
number we obtain that all values of the eigenfunction are uniquiely determined
under some supplementary conditions.
