Generalized semifield spreads

Anbar Meidl, Nurdagül and Kalaycı, Tekgül and Meidl, Wilfried (2023) Generalized semifield spreads. Designs, Codes, and Cryptography, 91 (2). pp. 545-562. ISSN 0925-1022 (Print) 1573-7586 (Online)

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A (normal) bent partition of an n-dimensional vector space Vn(p) over the prime field Fp, is a partition of Vn(p) into an n/2-dimensional subspace U, and subsets A1, … , AK, such that every function f:Vn(p)→Fp with the following property, is a bent function: The preimage set f-1(c)={x∈Vn(p):f(x)=c} contains exactly K/p of the sets Ai for every c∈ Fp, and f is also constant on U. The classical examples are bent partitions from spreads or partial spreads, which have been known for a long time. Only recently (Meidl and Pirsic in Des Codes Cryptogr 89:75–89, 2021; Anbar and Meidl in Des Codes Cryptogr 90:1081–1101, 2022), it has been shown that (partial) spreads are not the only partitions with this remarkable property. Bent partitions have been presented, which generalize the Desarguesian spread, but provably do not come from any (partial) spread. In this article we show that also for some classes of semifields we can construct bent partitions, which similarly to finite fields and the Desarguesian spread, can be seen as a generalization of the semifield spread. Our results suggest that there are many partitions, which have similar properties as spreads.
Item Type: Article
Uncontrolled Keywords: Bent function; Bent partition; Dual bent function; Semifield; Spread; Walsh transform
Subjects: Q Science > QA Mathematics > QA150-272.5 Algebra
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Nurdagül Anbar Meidl
Date Deposited: 06 May 2023 19:31
Last Modified: 06 May 2023 19:31

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