Relations between the Local Weight Distributions of a Linear Block Code, Its Extended Code, and Its Even Weight Subcode

摘要

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