LRC码最小距离限的深入分析

为了增强最小距离限的精确性，缩小最小距离的范围，提出了两个新的最小距离限．首先，在局部修复码Singleton-like限的基础上，通过理论推导提出了第1种新的最小距离限，该新限适用于所有码字；其次，结合新提出的最小距离限和已经存在的最小距离限，推导出了第2种新的最小距离限，该新限适合更小范围码字；再次，通过理论公式推导，得出了在相同参数情况下各个最小距离限之间的关系．仿真结果表明，在相同码长、信息位和局部性的条件下，第1种新的最小距离限的性能和Singleton-like限一样好，第2种新的最小距离限优于已存在的最小距离限．

In-depth analysis of bounds on the minimum distance of LRCs

In order to enhance the precision of the minimum distance and narrow its scope, this paper proposes two new bounds on the minimum distance which apply to Locally Repairable Codes. First, one bound is proposed by theoretical derivation on the basis of the Singleton-like bound. Second, the other is proposed based on existing methods and the new one proposed, and it is smaller in scope. Third, the connections are proposed among minimum distance bounds. Finally, simulation results show that the first new proposed bound is no better than the Singleton-like bound and the other is better than existing bounds on the minimum distance.