期刊论文

Fan, Yun

英文

IEEE Transactions on Information Theory

0018-9448

2016

62

11

6342-6347

10.1109/TIT.2016.2602842

This work was supported by the National Natural Science Foundation of China under Grant 11271005. H. Liu was supported by the Excellent Doctorial Dissertation Cultivation Grant from Central China Normal University under Grant 2016YBZZ082.

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We introduce quasi-cyclic codes of index 1(1/3), and construct a class of such codes generated by pairs of polynomials. By investigating the pair of circulant matrices associated with the generator pair of polynomials, we obtain the generator matrix of any code of the class. Using a probabilistic method, we prove that, for any positive real number δsuch that the asymptotic GV-bound at 2δis greater than 1/2, the probability that the relative minimal distance of the code in the class is greater than δis almost 1;and the probability that the rate of the code equals to 1/4 is als...