2023/09/23 by Wang, Jiaxin, Fu, Fang-Wei, Wei, Yadi +1 · 1 citation
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2309.13395
Vectorial dual-bent functions have recently attracted some researchers' interest as they play a significant role in constructing partial difference sets, association schemes, bent partitions and linear codes. In this paper, we further study vectorial dual-bent functions F: Vn(p)→ Vm(p), where 2≤ m ≤ (n)/(2), Vn(p) denotes an n-dimensional vector space over the prime field \mathbbFp. We give new characterizations of certain vectorial dual-bent functions (called vectorial dual-bent functions with Condition A) in terms of amorphic association schemes, linear codes and generalized Hadamard matrices, respectively. When p=2, we characterize vectorial dual-bent functions with Condition A in terms of bent partitions. Furthermore, we characterize certain bent partitions in terms of amorphic association schemes, linear codes and generalized Hadamard matrices, respectively. For general vectorial dual-bent functions F: Vn(p)→ Vm(p) with F(0)=0, F(x)=F(-x) and 2≤ m ≤ (n)/(2), we give a necessary and sufficient condition on constructing association schemes. Based on such a result, more association schemes are constructed from vectorial dual-bent functions.