Twin bent functions, strongly regular Cayley graphs, and Hurwitz-Radon theory

TL;DR

This paper explores the relationship between twin bent functions derived from Clifford algebras, their associated strongly regular Cayley graphs, and connections to Hurwitz-Radon theory, revealing non-isomorphic graph structures.

Contribution

It establishes a link between Clifford algebra representations, bent functions, and strongly regular graphs, and proves non-isomorphism of certain Cayley graphs using Radon's theorem.

Findings

Sequences of Cayley graphs are strongly regular and share parameters.

Graphs in the two sequences are mostly non-isomorphic, except in the first three cases.

The non-isomorphism proof relies on Radon's theorem.

Abstract

The real monomial representations of Clifford algebras give rise to two sequences of bent functions. For each of these sequences, the corresponding Cayley graphs are strongly regular graphs, and the corresponding sequences of strongly regular graph parameters coincide. Even so, the corresponding graphs in the two sequences are not isomorphic, except in the first 3 cases. The proof of this non-isomorphism is a simple consequence of a theorem of Radon.