3 research outputs found
A Further Study of Vectorial Dual-Bent Functions
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 , where , denotes an
-dimensional vector space over the prime field . 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 , 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 with and , 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
A Further Study of Vectorial Dual-Bent Functions
Vectorial dual-bent functions have recently attracted some researchers\u27 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 , where , denotes an -dimensional vector space over the prime field . 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 , 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 with and , 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