  A new bound on the minimum distance of q-ary cyclic codes is proposed. It is
based on the description by another cyclic code with small minimum distance.
The connection to the BCH bound and the Hartmann--Tzeng (HT) bound is
formulated explicitly. We show that for many cases our approach improves the HT
bound. Furthermore, we refine our bound for several families of cyclic codes.
We define syndromes and formulate a Key Equation that allows an efficient
decoding up to our bound with the Extended Euclidean Algorithm. It turns out
that lowest-code-rate cyclic codes with small minimum distances are useful for
our approach. Therefore, we give a sufficient condition for binary cyclic codes
of arbitrary length to have minimum distance two or three and lowest code-rate
