Strongly Regular Graphs from Weakly Regular Plateaued Functions

This paper presents the first construction of strongly regular graphs and association schemes from weakly regular plateaued functions over the finite fields of odd characteristic. Indeed, we generalize the construction method of strongly regular graphs from weakly regular bent functions given by Chee et al. [Journal of Algebraic Combinatorics, 34(2), 251–266, 2011] to weakly regular plateaued functions. In this framework, we construct strongly regular graphs with three types of parameters from weakly regular plateaued functions with some homogeneous conditions. We also construct a family of association schemes of class p from weakly regular plateaued p-ary functions.