  The design of plateaued functions over $GF(2)^n$, also known as 3-valued
Walsh spectra functions (taking the values from the set $\{0, \pm 2^{\lceil
\frac{n+s}{2} \rceil}\}$), has been commonly approached by specifying a
suitable algebraic normal form which then induces this particular Walsh
spectral characterization. In this article, we consider the reversed design
method which specifies these functions in the spectral domain by specifying a
suitable allocation of the nonzero spectral values and their signs. We analyze
the properties of trivial and nontrivial plateaued functions (as affine
inequivalent distinct subclasses), which are distinguished by their Walsh
support $S_f$ (the subset of $GF(2)^n$ having the nonzero spectral values) in
terms of whether it is an affine subspace or not. The former class exactly
corresponds to partially bent functions and admits linear structures, whereas
the latter class may contain functions without linear structures. A simple
sufficient condition on $S_f$, which ensures the nonexistence of linear
structures, is derived and some generic design methods of nontrivial plateaued
functions without linear structures are given. The extended affine equivalence
of plateaued functions is also addressed using the concept of dual of plateaued
functions. Furthermore, we solve the problem of specifying disjoint spectra
(non)trivial plateaued functions of maximal cardinality whose concatenation can
be used to construct bent functions in a generic manner. This approach may lead
to new classes of bent functions due to large variety of possibilities to
select underlying duals that define these disjoint spectra plateaued functions.
An additional method of specifying affine inequivalent plateaued functions,
obtained by applying a nonlinear transform to their input domain, is also
given.
