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Research Article | Open Access |

Good Quasi-Cyclic Codes from Circulant Matrices Concatenation using a Heuristic Method

Author 1: Bouchaib AYLAJ Author 2: Said NOUH Author 3: Mostafa BELKASMI Author 4: Hamid ZOUAKI
International Journal of Advanced Computer Science and Applications (IJACSA) · Vol. 7, No. 9 · Published 2016

DOI: 10.14569/IJACSA.2016.070909

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Abstract

In this paper we present a method to search q circulant matrices; the concatenation of these circulant matrices with circulant identity matrix generates quasi-cyclic codes with high various code rate q/(q+1) (q an integer). This method searches circulant matrices in order to find the good quasi-cyclic code (QCC) having the largest minimum distance. A modified simulated annealing algorithm is used as an evaluator tool of the minimum distance of the obtained QCC codes. Based on this method we found 16 good quasi-cyclic codes with rates (1/2, 2/3 and 3/4), their estimated minimum distance reaches the lower bounds of codes considered to be the better linear block codes in Brouwer’s database.

Keywords

Circulant matrix quasi-cyclic Codes Minimum Distance Simulated Annealing Linear Error Correcting codes

How to Cite this Article

AYLAJ, B., NOUH, S., BELKASMI, M., & ZOUAKI, H. (2016). Good Quasi-Cyclic Codes from Circulant Matrices Concatenation using a Heuristic Method. International Journal of Advanced Computer Science and Applications, 7(9). https://doi.org/10.14569/IJACSA.2016.070909

AYLAJ, Bouchaib, et al.. "Good Quasi-Cyclic Codes from Circulant Matrices Concatenation using a Heuristic Method." International Journal of Advanced Computer Science and Applications, vol. 7, no. 9, 2016, https://doi.org/10.14569/IJACSA.2016.070909.

@article{AYLAJ2016,
  title     = {Good Quasi-Cyclic Codes from Circulant Matrices Concatenation using a Heuristic Method},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {7},
  number    = {9},
  year      = {2016},
  publisher = {The Science and Information Organization},
  author    = {Bouchaib AYLAJ and Said NOUH and Mostafa BELKASMI and Hamid ZOUAKI},
  doi       = {10.14569/IJACSA.2016.070909},
  url       = {https://doi.org/10.14569/IJACSA.2016.070909}
}

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Volume 17 No. 11, November 2026
Paper Submission Due October 25, 2026
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