Research Article Open Access

Efficient Decoding Algorithm for Binary Quadratic Residue Codes Using Reduced Permutation Sets

Hamza Boualame1, Mostafa Belkasmi1 and Idriss Chana2
  • 1 Department of Web and Mobile Engineering, ENSIAS College of Engineering, Mohammed V University, in Rabat, Morocco
  • 2 Department of Computer Science, Ecole Supérieure de Technologie Moulay-Ismail University, Meknes, Morocco


The Quadratic Residue (QR) codes have a rich mathematic structure. Unfortunately, their Algebraic Decoding (AD) is not generalizable for all QR codes. In this study, an efficient hard decoding algorithm is proposed to generalize the decoding of the binary systematic Quadratic Residue (QR) codes. The proposed decoder corrects t erroneous bits or less, in the received word, based on a reduced set of permutations derived from the large automorphism group of QR codes. This set of permutations is applied to the received word to move the error positions and trap all of them in redundancy. Then, to evaluate the proposed method, we applied it to many binary QR codes of moderate code length starting with 17 until 113 with reducible and irreducible generator polynomials. The proposed decoder was validated by inserting all possible error patterns, that have t or less erroneous positions, as input of the proposed decoder and the output is always a correct codeword. The complexity study, in terms of the number of operations used, reveals that the light permutation decoding LPD algorithm significantly decreases decoding complexity without performance loss. So, it is qualified to be a good competitor to decode QR codes with lower lengths but is the best for QR codes with higher lengths.

Journal of Computer Science
Volume 19 No. 4, 2023, 526-539


Submitted On: 19 December 2022 Published On: 3 April 2023

How to Cite: Boualame, H., Belkasmi, M. & Chana, I. (2023). Efficient Decoding Algorithm for Binary Quadratic Residue Codes Using Reduced Permutation Sets. Journal of Computer Science, 19(4), 526-539.

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  • Automorphism Group
  • Permutation Decoding
  • Quadratic Residue Codes
  • Syndrome Decoding