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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 of failed nodes and parallel(More)
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)
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 paper 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<sup>(&#x03B4;-1)</sup>(More)
An (r, t)-locally repairable code satisfies a property that the value at each coordinate can be recovered from t disjoint repair sets each containing at most r other coordinates. This property is extremely useful in distributed storage systems for hot data. In this paper, we propose two constructions of (r, t)-LRCs. The first one is a cyclic code of which(More)
For binary [n, k, d] linear locally repairable codes (LRCs), two new upper bounds on k are derived. The first one applies to LRCs with disjoint local repair groups, for general values of n, d and locality r, containing some previously known bounds as special cases. The second one is based on solving an optimization problem and applies to LRCs with arbitrary(More)
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