  Binary duadic codes are an interesting subclass of cyclic codes since they
have large dimensions and their minimum distances may have a square-root bound.
  In this paper, we present several families of binary duadic codes of length
$2^m-1$ and develop some lower bounds on their minimum distances by using the
BCH bound on cyclic codes, which partially solves one case of the open problem
proposed in \cite{LLD}. It is shown that the lower bounds on their minimum
distances are close to the square root bound. Moreover, the parameters of the
dual and extended codes of these binary duadic codes are investigated.
