二元局部修复码的新构造  

The New Constructions of Binary Locally Repairable Codes

作　　者：杨森[1] 李瑞虎[1] 付强[1] 吕良东 YANG Sen;LI Ruihu;FU Qiang;LU Liangdong(Department of Basic Sciences,Air Force Engineering University,Xi’an 710051,China)

机构地区：[1]空军工程大学基础部

出　　处：《空军工程大学学报（自然科学版）》2019年第6期104-108,共5页Journal of Air Force Engineering University(Natural Science Edition)

基　　金：国家自然科学基金(11471011;11801564;11901579)

摘　　要：局部修复码(Locally Repairable Codes,简记为LRCs)是一种可以减小分布式存储系统修复带宽的新型纠删码。依据二元最优码的不同距离特性而改变校验矩阵的方法,提出了由奇距离局部修复码扩展构造偶距离局部修复码的一种方法;而且提出了通过删截的方法构造新的性能优良的局部修复码。利用这两种方法,构造出四组码长为n≤24,维数为k≥8且距离为6≤d≤8具有较小局部修复度的码,这些码都达到了C-M界。这些结果对于研究更大距离的二元最优局部修复码以及一般域上的最优局部修复码的构造,将具有借鉴意义。Locally repairable code(LRC)is a new family of erasure codes to reduce the repair bandwidth during recovering the lost data in distributed storage systems.Dependent on the characters of different distance and the parity check matrices of binary optimal codes,a method is presented to construct even-distance LRCs from odd-distance LRCs,and some new LRCs with good properties are obtained by puncturing strategy.By using these two methods,four classes of LRCs(length n≤24,dimension k≥8 and distance 6≤d≤8)attained to the C-M bound are constructed.There is much in these methods of constructing LRCs that optimal LRCs with higher distance over binary field and general fields can be made use of.

关 键 词：局部修复码 局部修复度 校验矩阵 二元最优线性码 C-M界 

分 类 号：O157.4[理学—数学]