  Polar code, with explicit construction and recursive structure, is the latest
breakthrough in channel coding field for its low-complexity and theoretically
capacity-achieving property. Since polar codes can approach the maximum
likelihood performance under successive cancellation list decoding (SCLD), its
decoding performance can be evaluated by Bonferroni-type bounds (e.g., union
bound) in which the Hamming weight spectrum will be used. Especially, the polar
codewords with minimum Hamming weight (PC-MHW) are the most important item in
that bound because they make major contributions to the decoding error pattern
particularly at high signal-to-noise-ratio. In this work, we propose an
efficient strategy for enumerating the PC-MHW and its number. By reviewing the
inherent reason that PC-MHW can be generated by SCLD, we obtain some common
features of PC-MHW captured by SCLD. Using these features, we introduce a
concept of zero-capacity bit-channel to obtain a tight upper bound for the
number of PC-MHW, whose computing complexity is sublinear with code length.
Furthermore, we prove that the proposed upper bound is really the exact number
of PC-MHW in most cases. Guided by the bound and its theoretical analysis, we
devise an efficient SCLD-based method to enumerate PC-MHW, which requires less
than half of the list size compared with the existing methods.
