  The asymptotic performance of a polar code under successive cancellation
decoding is determined by the exponent of its polarizing matrix. We first prove
that the partial distances of a polarizing matrix constructed from the
Kronecker product are simply expressed as a product of those of its component
matrices. We then show that the exponent of the polarizing matrix is shown to
be a weighted sum of the exponents of its component matrices. These results may
be employed in the design of a large polarizing matrix with high exponent.
