Amorphic association schemes from bent partitions

Anbar Meidl, Nurdagül and Kalaycı, Tekgül and Meidl, Wilfried (2024) Amorphic association schemes from bent partitions. Discrete Mathematics, 347 (1). ISSN 0012-365X (Print) 1872-681X (Online)

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Bent partitions are partitions of an elementary abelian group, which have similarities to partitions from spreads. In fact, a spread partition is a special case of a bent partition. In particular, bent partitions give rise to a large number of (vectorial) bent functions. Examples of bent partitions, which generalize the Desarguesian spread, have been presented by Anbar, Meidl and Pirsic, 2021, 2022. Bent partitions, which generalize some other classes of (pre)semifield spreads, have been presented by Anbar, Kalaycı, Meidl 2023. In this article, it is shown that these bent partitions induce (pk+1)-class amorphic associations schemes on Fpm×Fpm, where k is a divisor of m with special properties. This implies a construction of amorphic association schemes from some classes of (pre)semifields.
Item Type: Article
Uncontrolled Keywords: Association schemes; Bent functions; Bent partitions; Partial difference sets; Semifields; Strongly regular graphs
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Nurdagül Anbar Meidl
Date Deposited: 06 Feb 2024 14:33
Last Modified: 06 Feb 2024 14:33

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