Graphs of Vectorial Plateaued Functions as Difference Sets
| Autor: | ��e��melio��lu, Ay��a, Olmez, Oktay |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1807.11181 |
| Popis: | A function $F:\mathbb{F}_{p^n}\rightarrow \mathbb{F}_{p^m},$ is a vectorial $s$-plateaued function if for each component function $F_{b}(��)=Tr_n(��F(x)), b\in \mathbb{F}_{p^m}^*$ and $��\in \mathbb{F}_{p^n}$, the Walsh transform value $|\widehat{F_{b}}(��)|$ is either $0$ or $ p^{\frac{n+s}{2}}$. In this paper, we explore the relation between (vectorial) $s$-plateaued functions and partial geometric difference sets. Moreover, we establish the link between three-valued cross-correlation of $p$-ary sequences and vectorial $s$-plateaued functions. Using this link, we provide a partition of $\mathbb{F}_{3^n}$ into partial geometric difference sets. Conversely, using a partition of $\mathbb{F}_{3^n}$ into partial geometric difference sets, we constructed ternary plateaued functions $f:\mathbb{F}_{3^n}\rightarrow \mathbb{F}_3$. We also give a characterization of $p$-ary plateaued functions in terms of special matrices which enables us to give the link between such functions and second-order derivatives using a different approach. regular research paper |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|