ON A CLASS OF PRIMITIVE BCH-CODES

-We introduce a special class of primitive BCH codes, the minimal BCH (MB) codes. Let C be an MB code of length pmr— 1 and designed distance d over GF (q), q = pr; then d = aY,”=oqi where q - a is minimal in a certain sense. We prove that an MB code so defined has as minimum distance its designed distance. Using the Roos bound, we propose a lower bound, sometimes tight, for the minimum distance of the dual of an MB code. We describe the subclass of weakly self-dual extended MB codes and then characterize some weakly self-dual extended BCH codes. Similarly, we prove that the nontrivial extended MB code over GF(4) is the smallest extended BCH code which is not an even code. We point out that extended MB codes are principal ideals of a modular algebra of type Fpr[FPm]. © 1990 IEEE