In this letter, we derive a theorem which generalizes Theorem 3 in Chapter
9 of the book "The Theory of Error-Correcting Codes" by F. J. MacWilliams a
nd N. J. A, Sloane, By this theorem, we are able to give several classes of
BCH codes of composite length whose minimum distance does not exceed the B
CH bound. Moreover, we show that this theorem can also be used to determine
the true minimum distance of some other cyclic codes with composite-length
.