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A new efficient way based on special stabilizer multiplier permutations to attack the hardness of the minimum weight search problem for large BCH codes
International Journal of Electrical and Computer Engineering (IJECE) · Vol. 9 No. 2 (2019)
- ISSN
- 2088-8708, 2088-8708
- Published
- 2019-04-01
- Publisher
- Institute of Advanced Engineering and Science
Abstract
BCH codes represent an important class of cyclic error-correcting codes; their minimum distances are known only for some cases and remains an open NP-Hard problem in coding theory especially for large lengths. This paper presents an efficient scheme ZSSMP (Zimmermann Special Stabilizer Multiplier Permutation) to find the true value of the minimum distance for many large BCH codes. The proposed method consists in searching a codeword having the minimum weight by Zimmermann algorithm in the sub codes fixed by special stabilizer multiplier permutations. These few sub codes had very small dimensions compared to the dimension of the considered code itself and therefore the search of a codeword of global minimum weight is simplified in terms of run time complexity. ZSSMP is validated on all BCH codes of length 255 for which it gives the exact value of the minimum distance. For BCH codes of length 511, the proposed technique passes considerably the famous known powerful scheme of Canteaut and Chabaud used to attack the public-key cryptosystems based on codes. ZSSMP is very rapid and allows catching the smallest weight codewords in few seconds. By exploiting the efficiency and the quickness of ZSSMP, the true minimum distances and consequently the error correcting capability of all the set of 165 BCH codes of length up to 1023 are determined except the two cases of the BCH(511,148) and BCH(511,259) codes. The comparison of ZSSMP with other powerful methods proves its quality for attacking the hardness of minimum weight search problem at least for the codes studied in this paper.
Collaboration network of the authors
21 authors · 48 co-authorship links · 7 across different organisations
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- University of Hassan II Casablanca
- Mohammed V University
- Affiliation unknown
- Different organisations
- Same organisation
- Affiliation unknown
- Thicker line = more joint articles · bigger circle = more articles
Show as table
| Co-author | Organisation | Joint articles |
|---|---|---|
| Abdelali Zakrani | University of Hassan II Casablanca | 2 |
| Boulchahoub Hassan | Affiliation unknown | 1 |
| Amina Rachiq | Affiliation unknown | 1 |
| Amine Labriji | Affiliation unknown | 1 |
| Labriji Elhoussin | Affiliation unknown | 1 |
| Seddiq El Kasmi Alaoui | University of Hassan II Casablanca | 1 |
| Zouhair Chiba | University of Hassan II Casablanca | 1 |
| Hamza Faham | University of Hassan II Casablanca | 1 |
| Mohammed El Assad | University of Hassan II Casablanca | 1 |
| Salsabila Benghazouani | University of Hassan II Casablanca | 1 |
| Ihsane Haloum | University of Hassan II Casablanca | 1 |
| Mostafa Jebbar | University of Hassan II Casablanca | 1 |
| Jamal Eddine Rafiq | University of Hassan II Casablanca | 1 |
| Mohammed Amraouy | Mohammed V University | 1 |
| Abdellah Bennane | Mohammed V University | 1 |
| Bouchaib Aylaj | Affiliation unknown | 1 |
| Mostafa Belkasmi | Mohammed V University | 1 |
Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.