  The key step of generating the well-known Hsiao code is to construct a
{0,1}-check-matrix in which each column contains the same odd-number of 1's and
each row contains the same number of 1's or differs at most by one for the
number of 1's. We also require that no two columns are identical in the matrix.
The author solved this problem in 1986 by introducing a type of recursively
balanced matrices. However, since the paper was published in Chinese, the
solution for such an important problem was not known by international
researchers in coding theory. In this note, we focus on how to practically
generate the check matrix of Hsiao codes. We have modified the original
algorithm to be more efficient and effective. We have also corrected an error
in algorithm analysis presented in the earlier paper. The result shows that the
algorithm attained optimum in average cases if a divide-and-conquer technique
must be involved in the algorithm.
