An Algorithm for Computing the Local Distance Profile of Binary Linear Codes Closed under a Group of Permutations

摘要

We propose an algorithm for computing the local distance profile of binary linear codes which are closed under a group of permutations. An invariance property is used in the algorithm, which is an extension of the invariance property used in a known algorithm for binary cyclic codes. To use the extended invariance property, the proposed algorithm regards the code as the set of cosets of a subcode. The set of cosets are partitioned into equivalence classes by the invariance property. Only the local distance subprofile for the representative coset in each equivalence class is computed. We apply the algorithm to the (128, k) extended primitive BCH codes, and obtain the local distance profile of codes for k ≤ 43.