Bent Partitions And Lp-Packings

This thesis investigates the recently introduced concepts of bent partitions, LPpackings,and their interrelations, including their connection to vectorial dual-bentfunctions. We begin by showing that LP-packings give rise to (normal) bent partitions.Using examples involving ternary bent functions, we demonstrate that LPpackingsand bent partitions represent fundamentally different concepts.We then extend a known lifting procedure from Desarguesian spreads to LP-packingsin non-elementary abelian groups to a lifting procedure from generalized Desarguesianspreads to LP-packings in non-elementary abelian groups as well as largerelementary abelian groups. This generalization broadens the scope of known constructionsof LP-packings.In the final part, we explore secondary constructions of a class of vectorial dual-bentfunctions corresponding to bent partitions with a specific property. One constructionis based on the direct sum of vectorial functions, while the other generalizes a methodoriginally introduced by Wang, Fu, and Wei in [34]. These approaches yield a widevariety of vectorial bent functions, bent partitions,