  A cubelike graph is a Cayley graph on the product
$\mathbb{Z}_2\times\cdots\times\mathbb{Z}_2$ of the integers modulo $2$ with
itself finitely many times. In 1992, Payan proved that no cubelike graph can
have chromatic number $3$. The authors of the present paper previously
developed a general matrix method for studying chromatic numbers of Cayley
graphs on abelian groups. In this note, we apply this method of Heuberger
matrices to give an alternate proof of Payan's theorem.
