Bent Partition, Vectorial Dual-Bent Function, and LP-Packing Constructions

We present secondary constructions of vectorial functions respectively partitions of elementary abelian groups, which simultaneously yield vectorial dual-bent functions with certain properties, bent partitions, and under some conditions, Latin square partial difference set packings (LP-packings). First, we analyse constructions via the direct sum of vectorial functions and then present a version of the generalized Maiorana-McFarland construction. Next, we generalize a construction of vectorial dual-bent functions by Wang, Fu, and Wei (2023). Finally, we use a lifting procedure of LP-packings from Jedwab and Li (2021) to construct vectorial dual-bent functions, bent partitions, and LP-packings in elementary abelian groups. With these constructions, a large variety of vectorial bent functions, bent partitions, LP-packings, and related amorphic association schemes can be obtained.