Bent partitions

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