A Paley-like graph in characteristic two

TL;DR

This paper explores an analogue of the Paley graph over fields of even order, investigating its properties and noting features like Hamiltonian decomposition, to extend understanding of pseudo-random graphs in characteristic two.

Contribution

It introduces a new construction of a Paley-like graph in characteristic two and analyzes its properties, including Hamiltonian decomposition.

Findings

Existence of a Hamiltonian decomposition in the new graph

Properties analogous to classical Paley graphs in even characteristic

Initial insights into pseudo-randomness in characteristic two

Abstract

The Paley graph is a well-known self-complementary pseudo-random graph, defined over a finite field of odd order. We describe an attempt at an analogous construction using fields of even order. Some properties of the graph are noted, such as the existence of a Hamiltonian decomposition.