  Classical BCH codes that contain their (Euclidean or Hermitian) dual codes
can be used to construct quantum stabilizer codes; this correspondence studies
the properties of such codes. It is shown that a BCH code of length n can
contain its dual code only if its designed distance d=O(sqrt(n)), and the
converse is proved in the case of narrow-sense codes. Furthermore, the
dimension of narrow-sense BCH codes with small design distance is completely
determined, and - consequently - the bounds on their minimum distance are
improved. These results make it possible to determine the parameters of quantum
BCH codes in terms of their design parameters.
