Strongly regular graphs from weakly regular plateaued functions

TL;DR

This paper introduces new methods to construct strongly regular graphs and association schemes using weakly regular plateaued functions over finite fields, expanding the known connections between these functions and combinatorial structures.

Contribution

It generalizes previous constructions from bent functions to plateaued functions, enabling the creation of new strongly regular graphs and association schemes.

Findings

Constructed strongly regular graphs with three parameter types

Developed association schemes of class p from p-ary plateaued functions

Extended the construction framework to weakly regular plateaued functions

Abstract

The paper provides the first constructions of strongly regular graphs and association schemes from weakly regular plateaued functions over finite fields of odd characteristic. We generalize the construction method of strongly regular graphs from weakly regular bent functions given by Chee et al. in [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 p-ary plateaued functions.