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The design of plateaued functions over $GF(2)^n$, also known as 3-valuedWalsh spectra functions (taking the values from the set $\{0, \pm 2^{\lceil\frac{n+s}{2} \rceil}\}$), has been commonly approached by specifying asuitable algebraic normal form which then induces this particular Walshspectral characterization. In this article, we consider the reversed designmethod which specifies these functions in the spectral domain by specifying asuitable allocation of the nonzero spectral values and their signs. We analyzethe properties of trivial and nontrivial plateaued functions (as affineinequivalent distinct subclasses), which are distinguished by their Walshsupport $S_f$ (the subset of $GF(2)^n$ having the nonzero spectral values) interms of whether it is an affine subspace or not. The former class exactlycorresponds to partially bent functions and admits linear structures, whereasthe latter class may contain functions without linear structures. A simplesufficient condition on $S_f$, which ensures the nonexistence of linearstructures, is derived and some generic design methods of nontrivial plateauedfunctions without linear structures are given. The extended affine equivalenceof plateaued functions is also addressed using the concept of dual of plateauedfunctions. Furthermore, we solve the problem of specifying disjoint spectra(non)trivial plateaued functions of maximal cardinality whose concatenation canbe used to construct bent functions in a generic manner. This approach may leadto new classes of bent functions due to large variety of possibilities toselect 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 alsogiven.

Designing plateaued Boolean functions in spectral domain and their classification