Determination of the Local Weight Distribution of Binary Linear Block Codes

Abstract

Some methods to determine the local weight distribution of binary linear codes are presented. Two approaches are studied: A computational approach and a theoretical approach. For the computational approach, an algorithm for computing the local weight distribution of codes using the automorphism group of the codes is devised. In this algorithm, a code is considered the set of cosets of a subcode, and the set of cosets is partitioned into equivalence classes. Thus, only the weight distributions of zero neighbors for each representative coset of equivalence classes are computed. For the theoretical approach, relations between the local weight distribution of a code, its extended code, and its even weight subcode are studied. As a result, the local weight distributions of some of the extended primitive Bose-Chaudhuri-Hocquenghen (BCH) codes, Reed-Muller codes, primitive BCH codes, punctured Reed-Muller codes, and even weight subcodes of primitive BCH codes and punctured Reed-Muller codes are determined