Classifying bent functions by their Cayley graphs

Abstract

In 1999 Bernasconi and Codenotti noted that the Cayley graph of a bent function is strongly regular. This paper describes the concept of extended Cayley equivalence of bent functions, discusses some connections between bent functions, designs, and codes, and explores the relationship between extended Cayley equivalence and extended affine equivalence. SageMath scripts and CoCalc worksheets are used to compute and display some of these relationships, for bent functions up to dimension 8.