  In this paper, we derive the exact weight distributions that emerge during
each stage of successive cancellation decoding of polar codes. Though we do not
compute the distance spectrum of polar codes, the results allow us to get an
estimate of the decoding error probability and to show a link between the first
nonzero components of the weight distribution and the partial order between the
synthetic channels. Also, we establish the minimal distance between two cosets
associated with two paths that differ in two positions. This can be regarded as
a first step toward analyzing the weight distributions for the successive
cancellation list decoding.
