Secondary constructions of plateaued Boolean functions through addition of indicatorsPašalić, Enes (Avtor) Kudin, Sadmir (Avtor) Hodžić, Samir (Avtor) Khan, Dilawar Abbas (Avtor) plateaued functionslinear structuresGMM classRecently, the design of $s$-plateaued functions over $\F_2^n$, whose Walsh spectra take values in ${0,\pm 2^{\frac{n+s}{2}}}$, has been studied algorithmically to identify balanced plateaued functions of maximal algebraic degree, called optimal. In this article, we characterize optimal plateaued functions within the Generalized Maiorana-McFarland (GMM) class and provide sufficient conditions for them to have no nonzero linear structures. By adapting a technique of C. Carlet for modifying bent functions in the Maiorana-McFarland ($\cM$) class, we derive new classes of plateaued functions from $GMM$, including the subclass $\cD_0$ when $\phi$ is non-injective, although under more restrictive conditions. We also identify conditions ensuring plateauedness in the resulting $\cC$ class. Finally, using indicator functions of the form $1_{E_1}(x)1_{E_2}(y)$ for suitably chosen subspaces $E_1\subseteq\F_2^k$ and $E_2\subseteq\F_2^{n-k}$, we construct plateaued functions outside GMM.20262026-08-19 12:06:01Članek v reviji23520sl