  In their recent paper "The spectral norm of a Horadam circulant matrix",
Merikoski, Haukkanen, Mattila and Tossavainen study under which conditions the
spectral norm of a general real circulant matrix ${\bf C}$ equals the modulus
of its row/column sum. We improve on their sufficient condition until we have a
necessary one. Our results connect the above problem to positivity of
sufficiently high powers of the matrix ${\bf C^\top C}$. We then generalize the
result to complex circulant matrices.
