两类小码长四元局部修复码的构造OA

Efficient data repair is of great significance in distributed storage systems,and locally repairable codes(LRCs)can effectively enhance repair efficiency.Firstly,projective caps are utilized to construct LRCs with a code length 127≤n≤252 and a distance of 4.It is proved that all the constructed LRCs a-chieve either the Singleton-Like bound or the Cadambe-Mazumdar bound,i.e.,they are Singleton-Like(S-L)optimal or Cadambe-Mazumdar(C-M)optimal.Secondly,based on the generator matrices of some known optimal linear codes(BKLCs)with a dimension of 5,multiple methods are adopted to construct LRCs with small locality when the code length is length 25≤n≤110.It is also proved that some of these constructed LRCs are C-M optimal.