2,312 research outputs found
Generalized bent Boolean functions and strongly regular Cayley graphs
In this paper we define the (edge-weighted) Cayley graph associated to a
generalized Boolean function, introduce a notion of strong regularity and give
several of its properties. We show some connections between this concept and
generalized bent functions (gbent), that is, functions with flat Walsh-Hadamard
spectrum. In particular, we find a complete characterization of quartic gbent
functions in terms of the strong regularity of their associated Cayley graph.Comment: 13 pages, 2 figure
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
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