
Mathematical Research Seminar
Mathematical research seminar is organized by the departments of Mathematics of two members of the University - UP FAMNIT and Andrej Marušič Institute (UP IAM), every Monday from October to June.
You are cordially invited to attend the lectures.
This talk focuses on the construction of two new classes of plateaued functions, denoted by $\mathcal{C}$ and $\mathcal{D}_0$, both of which are derived from the $\mathcal{GMM}$ class. We introduce the class $\mathcal{C}$ of $s$-plateaued functions defined as
$$f(x, y) = x \cdot \phi(y) + 1_{L^{\perp}}(y),$$
where $0 < s < n$ and $L^{\perp}$ is a linear subspace of $\mathbb{F}_2^{\frac{n+s}{2}}$. This class is presented as a special subclass of the broader $\mathcal{D}$ class.
Furthermore, we demonstrate that the subclass $\mathcal{D}_0$ can still be constructed even when the mapping $\phi$ is not injective. However, in this case, the sufficient conditions are more complicated than in the bent function.
In the final part of the talk, I present an initial approach for decomposing a plateaued function $f \in \mathcal{B}_n$ into four component functions $f_i \in \mathcal{B}_{n-2}$, for $i \in [1, 4]$. The 4-decomposition of a plateaued function $f = f1||f2||f3||f4 \in \cB_n$ is explained by describing three atmost cases:
- All component functions $f_i \in \mathcal{B}_{n-2}$ $(i \in [1, 4])$ are plateaued.
- All $f_i$ are functions with $5$-valued Walsh spectra.
- A mixed 4-decomposition.
This is a joint work with Enes Pasalic and Sadmir Kudin.