Locality of Some Optimal Ternary Codes

The locality of a locally repairable code for a distributed storage system is the number of nodes that participate in the repair of failed nodes, which characterizes the repair cost. In this paper, using two ternary C 14 = [14,6,6]3 and C 19 = [19,6,9]3 codes with short lengths, we first construct optimal [447,6,290]3 and [406,6,270]3 codes with locality r=2. Then by constructing different anticodes using ternary codes with low dimensions, ten optimal codes with locality r=2 are obtained. Finally, we derive three optimal codes from every optimal code we have constructed and determine their locality r=2.