Locality of Some Optimal Ternary Linear Codes

A code whose every codeword symbol can be recovered from other certain symbols is called a locally repairable code (LRC). The locality of a locally repairable code for a distributed storage system is the number of nodes that participate in the repair process, which characterizes the repair cost. In this paper, firstly, some LRCs with locality r = 2 generated by special matrices are proved, and some methods of constructing generator matrix are proposed. Next, we construct generator matrices of k-dimensional optimal ternary linear codes and obtain their locality (k ≤ 4). Many optimal codes with small locality have been found.