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

Narrow-Sense BCH Codes over $\gf(q)$ with Length $n=\frac{q^m-1}{q-1}$