The author introduces a special class of primitive BCH codes, the minimal BCH (MB) codes. It is proved that an MB code has as minimum distance its designed distance. Using the Roos bound, the author proposes a lower bound, sometimes tight, for the minimum distance of the dual of an MB code. He describes the subclass of weakly self-dual extended MB codes and then characterizes some weakly self-dual extended BCH codes. Similarly, he proves that the nontrivial extended MB code over GF(4) is the smallest extended BCH code which is not an even code. He points out that extended MB codes are principal ideals of a modular algebra. >