  Cyclic codes over finite fields are widely employed in communication systems,
storage devices and consumer electronics, as they have efficient encoding and
decoding algorithms. BCH codes, as a special subclass of cyclic codes, are in
most cases among the best cyclic codes. A subclass of good BCH codes are the
narrow-sense BCH codes over $\gf(q)$ with length $n=(q^m-1)/(q-1)$. Little is
known about this class of BCH codes when $q>2$. The objective of this paper is
to study some of the codes within this class. In particular, the dimension, the
minimum distance, and the weight distribution of some ternary BCH codes with
length $n=(3^m-1)/2$ are determined in this paper. A class of ternary BCH codes
meeting the Griesmer bound is identified. An application of some of the BCH
codes in secret sharing is also investigated.
