An efficient method to find the minimum distance of linear block codes

Abstract

Finding the minimum distance of linear codes is in general a NP-hard problem, we propose an efficient algorithm to attack this problem. The principle of this approach is to search code words locally around the all-zero code word perturbed by a level of noise magnitude, in other words the maximum of noise that can be corrected by a Soft-In decoder, anticipating that the resultant nearest non-zero code words will most likely contain the minimum Hamming weight code word, whose Hamming weight is equal to the minimum distance of the linear code. A numerous results prove that the proposed algorithm is valid for general linear codes and it is very fast comparing to all others known techniques, therefore it is a good tool for computing. Comparing to Joanna's works, we proof that our algorithm has a low complexity with a fast time of execution. For some linear RQs, QDCs and BCHs codes with unknown minimum distance, we give a good estimation (true) of the minimum distance where the length is less than 439.