  Whereas the design and properties of bent and plateaued functions have been
frequently addressed during the past few decades, there are only a few design
methods of so-called 5-valued spectra Boolean functions whose Walsh spectra
takes the values in $\{0, \pm 2^{\lambda_1}, \pm 2^{\lambda_2}\}$. Moreover,
these design methods mainly regards the specification of these functions in
their ANF (algebraic normal form) domain. In this article, we give a precise
characterization of this class of functions in their spectral domain using the
concept of a dual of plateaued functions. Both necessary and sufficient
conditions on the Walsh support of these functions are given which then
connects their design (in spectral domain) to a family of so-called {\em
totally (non-overlap) disjoint spectra plateaued functions}. We identify some
suitable families of plateaued functions having this property, thus providing
some generic methods in the spectral domain. Furthermore, we also provide an
extensive analysis of their constructions in the ANF domain and provide several
generic design methods. The importance of this class of functions is
manifolded, where apart from being suitable for some cryptographic applications
we emphasize their property of being constituent functions in the so-called
4-bent decomposition.
