Analysis of some classes of bent partitions and vectorial bent functions

Official URL: https://dx.doi.org/10.1007/s10623-026-01835-9

Since the introduction of bent partitions by Anbar and Meidl (Des Codes Cryptogr 90:1081–1101, 2022), several constructions have been presented. All of them correspond to vectorial dual-bent functions with certain conditions, referred to as Condition A, and to partitions of a vector space into partial difference sets, respectively, to Latin square partial difference set packings (LP-packings). We provide the first constructions of bent partitions that do not induce partial difference sets, which shows that bent partitions and LP-packings are inequivalent concepts. We comprehensively analyse vectorial dual-bent functions in the extended Maiorana–McFarland class, which induce bent partitions and corresponding LP-packings. For two classes of bent partitions in characteristic 2, we show that every vectorial bent function from F2m×F2m to F2k, k<m, obtained from the bent partitions, can be lifted to a vectorial bent function mapping into F2m. We finally analyse two classes of vectorial bent function constructions.