Bent partitions and partial difference sets

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Anbar Meidl, Nurdagül and Kalaycı, Tekgül and Meidl, Wilfried (2022) Bent partitions and partial difference sets. IEEE Transactions on Information Theory, 68 (10). pp. 6894-6903. ISSN 0018-9448 (Print) 1557-9654 (Online)

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Abstract

The recently introduced concept of a bent partition of a 2m-dimensional vector space V(p) 2m over a prime field Fp exhibits similar properties as a partition from a spread. In particular, it gives rise to a large family of bent functions obtained in the same manner as spread bent functions. We show that the first non-spread construction of bent partitions introduced by Pirsic and the third author (p = 2), respectively, the first and the third author (p odd), gives rise to a large variety of different bent partitions. Especially, we show that the sets of bent functions obtained with any two such bent partitions do not intersect. We then show that every union of sets from one of these bent partitions always forms a partial difference set. This generalizes some known results on partial difference sets from spreads. Some general results on partial difference sets from bent partitions of V(2) 2m are given in the last section. IEEE
Item Type: Article
Uncontrolled Keywords: Bent functions; bent partitions; Boolean functions; characters; curves over finite fields; Indexes; partial difference sets; Standards; Transforms
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA150-272.5 Algebra
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Nurdagül Anbar Meidl
Date Deposited: 21 Sep 2022 10:59
Last Modified: 21 Sep 2022 10:59
URI: https://research.sabanciuniv.edu/id/eprint/44557

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