Locally repairable fractional repetition codes

In this paper, we propose three constructions of locally repairable codes based on fractional repetition (FR) codes. We also derive the bounds on the maximum file size stored with locally repairable FR codes with locality 2 and 3, respectively. Construction 1 results in a locally repairable FR code with locality 2. It has repetition degree ρ = 2, and attains the bound on the maximum file size we derived. The availability of this code is designed to be ρ - 1 = 1. Construction 2 results in a code which has larger availability ρ - 1 = 2 so that multiple node failures can be `locally´ repaired. This code also attains the bound on the maximum file size but with larger number of storage nodes. Construction 3 is a result of reducing the number of storage nodes.