PhD. Thesis Defense: Sezel Alkan
BENT PARTITIONS AND LP-PACKINGS
Sezel Alkan
Mathematics, PhD Dissertation, 2025
Thesis Jury
Asst. Prof. Dr. Nurdagül Anbar Meidl (Thesis Advisor)
Prof. Dr. Seher Tutdere Kavut
Asst. Prof. Dr. Ayesha Asloob Qureshi
Asst. Prof. Dr. Mohamed Dabagh
Asst. Prof. Dr. Süha Orhun Mutluergil
Date & Time: 17th, July 2025 – 2:00 PM
Place: FENS L035
Zoom link: https://sabanciuniv.zoom.us/j/
Keywords : Bent function, bent partition, LP-packing, partial difference set,
vectorial dual-bent function
Abstract
In this thesis, we study mainly on the recently introduced concepts bent partitons, LP-packings and their connections with each other, and also with vectorial dual-bent functions. First, we observe that LP-packings yield bent partitions. Then with some examples from ternary bent functions we show that normal bent partitions and LP-packings are different concepts. Next, we extend a lifting procedure from spreads to LP-packings in non-elementary abelian groups to a lifting procedure from generalized Desarguesian spreads to LP-packings in non-elementary abelian groups and in larger elementary abelian groups. In the last part, we analyze some secondary constructions of vectorial dual-bent functions satisfying a certain property. The first construction is via direct sum of vectorial functions and the other is a more general version of the construction of vectorial dual-bent functions given by Wang, Fu and Wei in 2023. With these constructions one can obtain a large variety of vectorial bent functions, bent partition and LP-packings.