Twin bent functions and Clifford algebras

TL;DR

This paper explores the relationship between twin bent functions and Clifford algebras, providing necessary conditions for automorphisms of edge-coloured graphs related to Clifford algebra representations.

Contribution

It introduces a novel connection between twin bent functions and Clifford algebra automorphisms, offering new necessary conditions for graph symmetries.

Findings

Identifies a necessary condition for automorphisms based on twin bent functions.

Examines additional necessary conditions related to Clifford algebra representations.

Establishes a link between bent functions and graph automorphisms in algebraic structures.

Abstract

This paper examines a pair of bent functions on $\mathbb{Z}_2^{2m}$ and their relationship to a necessary condition for the existence of an automorphism of an edge-coloured graph whose colours are defined by the properties of a canonical basis for the real representation of the Clifford algebra $\mathbb{R}_{m,m}.$ Some other necessary conditions are also briefly examined.