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—We give an explicit construction of exact cooperative regenerating codes at the MBCR (minimum bandwidth cooperative regeneration) point. Before the paper, the only known explicit MBCR code is given with parameters n = d+r and d = k, while our construction applies to all possible values of n, k, d, r. The code has a brief expression in the polynomial form… (More)

In distributed storage systems, erasure codes with locality r is preferred because a coordinate can be recovered by accessing at most r other coordinates which in turn greatly reduces the disk I/O complexity for small r. However, the local repair may be ineffective when some of the r coordinates accessed for recovery are also erased. To overcome this… (More)

—The ith coordinate of an (n, k) code is said to have locality r and availability t if there exist t disjoint groups, each containing at most r other coordinates that can together recover the value of the ith coordinate. This property is particularly useful for codes for distributed storage systems because it permits local repair and parallel accesses of… (More)

The locally repairable code (LRC) studied in this paper is an [n, k] linear code of which the value at each coordinate can be recovered by a linear combination of at most r other coordinates. The central problem in this work is to determine the largest possible minimum distance for LRCs. First, an integer programming based upper bound is derived for any… (More)

Repair locality is a desirable property for erasure codes in distributed storage systems. Recently, different structures of local repair groups have been proposed in the definitions of repair locality. In this paper, the concept of regenerating set is introduced to characterize the local repair groups. A definition of locality r (δ−1) (i.e., locality r with… (More)

—We present two new upper bounds on the dimension k for binary linear locally repairable codes (LRCs). The first one is an explicit bound for binary linear LRCs with disjoint repair groups, which can be regarded as an extension of known explicit bounds for such LRCs to more general code parameters. The second one is based on an optimization problem, and can… (More)

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