  Two generalizations of the Hartmann--Tzeng (HT) bound on the minimum distance
of q-ary cyclic codes are proposed. The first one is proven by embedding the
given cyclic code into a cyclic product code. Furthermore, we show that unique
decoding up to this bound is always possible and outline a quadratic-time
syndrome-based error decoding algorithm. The second bound is stronger and the
proof is more involved.
  Our technique of embedding the code into a cyclic product code can be applied
to other bounds, too and therefore generalizes them.
