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.
Highlights
In coding theory, a large side of research has been interested in design and construction of error correcting codes families which are the basis of the channel coding element in the digital communication system
We present in this paper, a method to search a good quasicyclic codes with rate q/(q+1) based in extensive random search for circulant matrices, and we chose the heuristic simulated annealing method (SA) to find the value of the minimum distance of quasi-cyclic codes that we have constructed
Step2: Generate q circulant matrices Ai related to TH Step3: Generate the Generator matrix G of the quasi-cyclic code related to Ai matrices Step4: Calculate the minimum distance dmin of the generated quasi-cyclic code using simulated annealing (In Algorithm 2) Step5: If take the Total Header TH
Summary
A large side of research has been interested in design and construction of error correcting codes families which are the basis of the channel coding element in the digital communication system. The design of good error correcting codes is a difficult problem, which remains open in coding theory. This problem is attacked with meta-heuristic methods. We present in this paper, a method to search a good quasicyclic codes with rate q/(q+1) (where q is an integer) based in extensive random search for circulant matrices, and we chose the heuristic simulated annealing method (SA) to find the value of the minimum distance of quasi-cyclic codes that we have constructed. We give an introduction on quasi-circulant codes, the minimum distance of linear block codes, encoding operations and simulated annealing method.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
