An Efficient method to find the Minimum Distance of Linear Block Codes

TitreAn Efficient method to find the Minimum Distance of Linear Block Codes
Publication TypeConference Paper
Year of Publication2012
AuthorsAskali, M, Nouh, S, Belkasmi, M
EditorEssaaidi, M, Zaz, Y
Conference Name2012 INTERNATIONAL CONFERENCE ON MULTIMEDIA COMPUTING AND SYSTEMS (ICMCS)
PublisherMorocco Sect MTT/AP Joint Chapter
ISBN Number978-1-4673-1520-3
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.

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