文章摘要
张茂1,李瑞虎1,宋倩2,陈刚3.短码长的五元最优局部修复码[J].空军工程大学学报:自然科学版,2020,21(3):106-110
短码长的五元最优局部修复码
Optimal Quinary Locally Repairable Codes with Small Code Length
  
DOI:
中文关键词: 局部修复码  最优码  Singleton形界
英文关键词: locally repairable codes  optimal LRC  Singleton like bound
基金项目:国家自然科学基金(11801564,11901579);空军工程大学基础部研究生创新基金
作者单位
张茂1,李瑞虎1,宋倩2,陈刚3 1.空军工程大学基础部西安7100512.兰州市27支局30信箱55号兰州7327503.75837部队广州,510000 
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中文摘要:
      在分布式存储系统中,应用局部修复码(LRCs),可以提高修复错误节点的效率。研究了码长不大于31的五元最优LRCs,给出了4类五元最优LRCs及其具体刻画。首先利用距离最优的线性码和Simplex码等特殊码,构造了性能较好的LRCs的校验矩阵。对已得到的LRCs,通过矩阵变换、矩阵拼接和删截的方法,给出了其他LRCs。所构造的五元LRCs的最小距离为2≤d≤8和d=10,参数均达到了Singleton界。这些结果对于其他五元最优LRCs和一般域上最优LRCs的构造具有借鉴意义。
英文摘要:
      The application of locally repairable codes (LRCs) in distributed storage system can improve the efficiency of repairing lost nodes. The optimal quinary LRCs with a code length of not more than 31 are studied and Four kinds of optimal quinary LRCs and their characterization are given. Firstly, parity check matrixes with good performance of LRCs are constructed by using the distance optimal linear codes and special codes such as Simplex code. For the known LRCs, other LRCs are given by means of shortening, puncturing, adding or deleting column vectors. The results show that these optimal LRCs have minimum distance 2≤d≤8 or d=10 and all the results respect the Singleton like bound. These results have reference value for the construction of other optimal quinary LRCs and optimal LRCs over general fields.
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