2025/09/21 by Jiaxin Wang, Wang, Jiaxin, Yadi Wei +3
Engineering · Mathematics · #Advanced Combinatorial Mathematics #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2509.16911
openalex publication_date 2025/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bent partitions of Vn(p) play an important role in constructing (vectorial) bent functions, partial difference sets, and association schemes, where Vn(p) denotes an n-dimensional vector space over the finite field \mathbbFp, n is an even positive integer, and p is a prime. For bent partitions, there remains a challenging open problem: Whether the depth of any bent partition of Vn(p) is always a power of p. Notably, the depths of all current known bent partitions of Vn(p) are powers of p. In this paper, we prove that for a bent partition Γ of Vn(p) for which all the p-ary bent functions generated by Γ are regular or all are weakly regular but not regular, the depth of Γ must be a power of p. We present new constructions of bent partitions that (do not) correspond to vectorial dual-bent functions. In particular, a new construction of vectorial dual-bent functions is provided. Additionally, for general bent partitions of Vn(2), we establish a characterization in terms of Hadamard matrices.