  We present a family of reducible cyclic codes constructed as the direct sum
of two different semiprimitive two-weight irreducible cyclic codes. This family
generalizes the class of reducible cyclic codes that was reported in the main
result of B. Wang, {\em et al.} \cite{once}. Moreover, despite of what was
stated therein, we show that, at least for the codes studied here, it is still
possible to compute the frequencies of their weight distributions through the
cyclotomic numbers in a very easy way.
