On the dimension and minimum distance of BCH codes over GF(q)

In this paper, only narrow-sense primitive BCH codes over GF(q) are considered. A formula, that can be used in many cases, is first presented for computing the dimension of BCH codes. It improves the result given by MacWilliams and Sloane in 1977. A new method for finding the dimension of all types of BCH codes is proposed. In second part, it is proved that the BCH bound is the leader of some cyclotomic coset, and we guess that the minimum distance for any BCH code is also the leader of some cyclotomic coset. Supported by the National Natural Science Foundation of China