基于sunflower的局部修复码构造

针对目前构造达到C-M界的二元局部修复码（LRC）的相关研究已经较为充分,但在一般域上还相对较少的问题,研究了一般域上LRC的构造。首先,提出了通过射影几何理论确定sunflower中元素个数的方法。其次,通过不相交局部修复组刻画LRC,从而清楚地描述LRC的码长、维数和局部度等参数。最后,在具有不相交局部修复组的校验矩阵的基础上,利用sunflower构造了两类一般域上最小距离为6的LRC,其中很多LRC是最优或拟最优的。相较于现有利用子域子码、广义级联码和代数曲线等方法构造的LRC,所构造得到的两类码在相同的码的最小距离和局部度下提升了信息率。这些结果说明所提方法可应用于一般域上其他LRC的构造。     

短码长四元最优局部修复码的构造

In distributed storage system, when a node fails, Locally Repairable Code (LRC) can access other nodes to recover data. However, the locality of LRC is not the same. Quaternary LRC with short code length and small locality is constructed. When code length is not more than 20 and minimum distance is greater than 2, if the dimension of generator matrix of a quaternary distance optimal linear code does not exceed the dimension of parity-check matrix, an LRC can be constructed from generator matrix, otherwise parity-check matrix can be used to construct an LRC. From generator matrices or parity-check matrices of LRCs constructed, other LRC are given by operations of deleting and juxtaposition. There are 190 LRC with code length n ≤ 20 and minimum distance d ≥ 2 to be constructed. Except for 12 LRC, other LRC are all locality optimal.