Bent partitions

Spread and partial spread constructions are the most powerful bent function constructions. A large variety of functions from a 2m-dimensional vector space $${\mathbb {V}}_{2m}^{(p)}$$ over {F}}_p$$ into can be generated, which constant on sets partition obtained with subspaces (partial) spread. Moreover, spreads one obtains not only between elementary abelian groups, but to B, where B any group order $$p^k$$ , $$k\le m$$ . As recently shown (Meidl, Pirsic 2021), partitions {V}}_{2m}^{(2)}$$ these remarkable properties. In this article we present first such partitions—other than spreads—which call partitions, for p odd. We investigate general properties like number cardinality subsets partition. show that construct cyclic {Z}}_{p^k}$$ With results, obtain odd, provably do come spreads.