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Said Nouh
Hassan II University
Computer Science & IT Electrical & Electronics Engineering

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Journal : International Journal of Electrical and Computer Engineering

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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 Issam Abderrahman Joundan; Said Nouh; Mohamed Azouazi; Abdelwahed Namir
International Journal of Electrical and Computer Engineering (IJECE) Vol 9, No 2: April 2019
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (552.357 KB) | DOI: 10.11591/ijece.v9i2.pp1232-1239

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.
Efficiency of two decoders based on hash techniques and syndrome calculation over a Rayleigh channel Seddiq El Kasmi Alaoui; Zouhair Chiba; Hamza Faham; Mohammed El Assad; Said Nouh
International Journal of Electrical and Computer Engineering (IJECE) Vol 13, No 2: April 2023
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijece.v13i2.pp1880-1890

Abstract

The explosive growth of connected devices demands high quality and reliability in data transmission and storage. Error correction codes (ECCs) contribute to this in ways that are not very apparent to the end user, yet indispensable and effective at the most basic level of transmission. This paper presents an investigation of the performance and analysis of two decoders that are based on hash techniques and syndrome calculation over a Rayleigh channel. These decoders under study consist of two main features: a reduced complexity compared to other competitors and good error correction performance over an additive white gaussian noise (AWGN) channel. When applied to decode some linear block codes such as Bose, Ray-Chaudhuri, and Hocquenghem (BCH) and quadratic residue (QR) codes over a Rayleigh channel, the experiment and comparison results of these decoders have shown their efficiency in terms of guaranteed performance measured in bit error rate (BER). For example, the coding gain obtained by syndrome decoding and hash techniques (SDHT) when it is applied to decode BCH (31, 11, 11) equals 34.5 dB, i.e., a reduction rate of 75% compared to the case where the exchange is carried out without coding and decoding process.
Co-Authors Abdelwahed Namir Hamza Faham Issam Abderrahman Joundan Mohamed Azouazi Mohammed El Assad Seddiq El Kasmi Alaoui Zouhair Chiba