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

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。

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.