Graphs of vectorial plateaued functions as difference sets

A function F:Fpn→Fpm, is a vectorial s-plateaued if for each component Fb(μ)=Trn(bF(x)),b∈Fpm⁎ and μ∈Fpn, the Walsh transform value |Fbˆ(μ)| either 0 or pn+s2. In this paper, we explore relation between (vectorial) functions partial geometric difference sets. Moreover, establish link three-valued cross-correlation of p-ary sequences functions. Using link, provide partition F3n into Conversely, using sets, construct ternary plateaued f:F3n→F3. We also give characterization in terms special matrices which enables us to such second-order derivatives different approach.