Binary Locally Repairable Codes - Sequential Repair for Multiple Erasures

Locally repairable codes (LRC) for distributed storage allow two approaches to locally repair multiple failed nodes: 1) parallel approach, by which each newcomer access a set of.. live nodes (r is the repair locality) to download data and recover the lost packet; and 2) sequential approach, by which the newcomers are properly ordered and each newcomer access a set of.. other nodes, which can be either a live node or a newcomer ordered before it. An [n,k] linear code with locality.. that allows local repair for up to.. failed nodes by sequential approach is called an (n,k,r,t)- exact locally repairable code (ELRC). In this paper, we present a family of binary codes which is equivalent to the direct product of.. copies of the [r + 1,r] singleparity- check code. We prove that such codes are (n,k,r,t)- ELRC with n = (r + 1)(m) , k = r(m) and t = 2(m) - 1, which implies that they permit local repair for up to 2(m) - 1 erasures by sequential approach. Our result shows that the sequential approach has much bigger advantage than parallel approach.