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Opis: Recently, 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.
Ključne besede: plateaued functions, linear structures, GMM class
Objavljeno v RUP: 19.08.2026; Ogledov: 445; Prenosov: 45
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Ključne besede: Plateaued functions, extended affine equivalence, extendable and nontrivial Plateaued functions
Objavljeno v RUP: 06.05.2020; Ogledov: 4430; Prenosov: 90
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Ključne besede: 5-valued spectra functions, bent functions, compositional representation, dual functions, plateaued functions, Walsh support
Objavljeno v RUP: 24.10.2019; Ogledov: 4470; Prenosov: 95
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