  We consider primitive aperiodic substitutions of constant length q and prove
that, in order to have a Lebesgue component in the spectrum of the associated
dynamical system, it is necessary that one of the eigenvalues of the
substitution matrix equals $\sqrt{q}$ in absolute value. The proof is based on
results of M. Queff\'elec, combined with estimates of the local dimension of
the spectral measure at zero.
