The Hamming distances of repeated-root cyclic codes of length 5p(s)
The Hamming distances of repeated-root cyclic codes of length 5p(s)
复制标题
长度为 5p(s) 的重根循环码的汉明距离
DOI：
10.1016/j.dam.2020.03.026
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发表时间：
2020
影响因子：
1.1
通讯作者：
Yue Qin
中科院分区：
文献类型：
--
作者：
Li Xia;Yue Qin
由于循环码在消费类电子产品、数据存储系统和通信系统中的广泛应用，循环码已成为编码理论中一个有趣的研究课题。设p是素数，且p≥ 7.我们确定了Fq上所有长度为5 ps的重复根循环码的汉明距离，其中q= pm，s和m都是正整数.此外，我们发现所有的MDS循环码的长度为5 ps和量子同步码的长度为5 ps的重复根循环码。通过比较5 ps长度重复根循环码与长度相近的BCH码的最小距离，说明了由重复根循环码构造的量子同步码在纠正Pauli错误方面比BCH码具有更好的性能.
Due to the wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. In this paper, let p be a prime with p≥ 7. We determine the Hamming distances of all repeated-root cyclic codes of length 5 p s over F q, where q= p m and both s and m are positive integers. Furthermore, we find all MDS cyclic codes of length 5 p s and take quantum synchronizable codes from repeated-root cyclic codes of length 5 p s. By comparing the minimum distances of 5 p s-length repeated-root cyclic codes to BCH codes of close lengths, we illustrated that quantum synchronizable codes constructed from repeated-root cyclic codes have in general better performance in correcting Pauli errors than those from BCH codes.