文章摘要
郑尤良, 李瑞虎, 吕京杰, 张茂.基于循环码的三元局部修复码构造[J].空军工程大学学报:自然科学版,2020,21(4):108-111
基于循环码的三元局部修复码构造
Constructions of Ternary Locally Repairable Codes Based on Cyclic Code
  
DOI:
中文关键词: 局部修复码  三元域  C-M界  循环码  定义集
英文关键词: locally repairable codes  ternary field  C-M bound  cyclic code  defining set
基金项目:国家自然科学基金(11901579)
作者单位
郑尤良, 李瑞虎, 吕京杰, 张茂 空军工程大学基础部西安710051 
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中文摘要:
      局部修复码(Locally Repairable Codes)是一种能为分布式存储系统提供信息修复能力的新型纠删码。针对目前三元域上局部修复码的研究尚不充分的情况,给出了利用循环码构造局部修复码的一般方法。首先从循环码的码长出发,计算出对应的3-分圆陪集,然后通过分圆陪集的组合确定各循环码的定义集从而确定码的距离和局部度,进而构造了码长8≤n≤50范围内达到Cadambe Mazumdar(C-M)界的三元局部修复码。特别是通过定义集设计对偶距离,并利用BCH界筛选分圆陪集,构造了3种具有小局部度的最优局部修复码。这些研究结果进一步完善了三元局部修复码的相关构造理论。
英文摘要:
      Locally repairable codes are a kind of new erasure codes capable of providing information repair ability for distributed storage systems. Aimed at the problem that the researches on the locally repairable codes are still insufficient in ternary field at present, a general method of constructing locally repairable codes based on cyclic codes is presented. Firstly, proceeded from the code length of cyclic codes, the corresponding 3 cyclotomic cosets are calculated, and then the defining sets of each cyclic codes are determined through the combinations of cyclotomic cosets, thus determining the distance and locality of codes, and constructing the three kinds locally repairable codes reaching Cadambe Mazumdar (C-M) bound with 8≤n≤50. Particularly, three kinds of optimal locally repairable codes with small locality are constructed by designing the dual distance through defining sets and by using BCH boundary to filter the circular coset. The relevant construction theory of ternary locally repairable codes is further being perfected by these research results.
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