A code is called $(n, k, r, t)$ information symbol locally repairable code (IS-LRC) if each information coordinate can be achieved by at least $t$ disjoint repair sets containing at most $r$ other coordinates. This letter considers a class of $(n, k, r, t)$ IS-LRCs, where each repair set contains exactly one parity coordinate. We explore the systematic code in terms of the standard parity check matrix. First, we propose some structural features of the parity check matrix by showing a connection with the membership matrix. After that, we place parity check matrix based proof of several bounds associated with the code. In addition, we provide two constructions of optimal parameters of $(n,k,r,t)$ IS-LRCs with the help of two Cayley tables of a finite field. Finally, we present a generalized result on optimal $q$-ary $(n,k,r,t)$ IS-LRCs related to MDS codes.

翻译：如果每项信息协调可以至少用美元来完成含有最多为美元的其他坐标的不连接修理装置,则代号为$(n, k, r, t)美元的信息符号当地可修理代码(IS-LRC)。本信考虑的是每套修理装置完全包含一个对等坐标的IS-LRC(n, k, r, t)美元类别。我们从标准对等检查矩阵的角度探索系统的代码。首先,我们通过显示与成员矩阵的联系,提出平价检查矩阵的一些结构特征。之后,我们设置了基于等价检查矩阵的与代码相关的若干界限的证据。此外,我们还在两个限定字段的Cayley表格的帮助下,提供了两套(n, k,r, t)美元IS-LRC($)的最佳参数。最后,我们对与MDS代码有关的最佳美元(n, k,r, t)IS-LRC(n, 美元)提出了普遍结果。