  Relations between the local weight distributions of a binary linear code, its
extended code, and its even weight subcode are presented. In particular, for a
code of which the extended code is transitive invariant and contains only
codewords with weight multiples of four, the local weight distribution can be
obtained from that of the extended code. Using the relations, the local weight
distributions of the $(127,k)$ primitive BCH codes for $k\leq50$, the
$(127,64)$ punctured third-order Reed-Muller, and their even weight subcodes
are obtained from the local weight distribution of the $(128,k)$ extended
primitive BCH codes for $k\leq50$ and the $(128,64)$ third-order Reed-Muller
code. We also show an approach to improve an algorithm for computing the local
weight distribution proposed before.
