We consider primitive cyclic codes of length p^m-1 over Fp. The codes of interest here are duals of BCH codes. For these codes, a lower bound on their minimum distance can be found via the adaptation of the Weil bound to cyclic codes. However, this bound is of no significance for roughly half of these codes. We shall fill this gap by giving, in the first part of the correspondence, a lower bound for an infinite class of duals of BCH codes. Since this family is a filtration of the duals of BCH codes, the bound obtained for it induces a bound for all duals. In the second part we present a lower bound obtained by implementing an algorithmic method due to Massey and Schaub (1988)-the rank-bounding algorithm. The numerical results are surprisingly higher than all previously known bounds