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

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.

Bouchaib AYLAJ, Said NOUH, Mostafa BELKASMI and Hamid ZOUAKI. “Good Quasi-Cyclic Codes from Circulant Matrices Concatenation using a Heuristic Method”. International Journal of Advanced Computer Science and Applications (IJACSA) 7.9 (2016). http://dx.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},
doi = {10.14569/IJACSA.2016.070909},
url = {http://dx.doi.org/10.14569/IJACSA.2016.070909},
year = {2016},
publisher = {The Science and Information Organization},
volume = {7},
number = {9},
author = {Bouchaib AYLAJ and Said NOUH and Mostafa BELKASMI and Hamid ZOUAKI}
}