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In an [n, k, d] linear code, a code symbol is said to have locality r if it can be repaired by accessing at most r other code symbols. For an (n, k, r) locally repairable code (LRC), the minimum distance satisfies the well-known Singleton-like bound d ≤ n − k − [k/r] + 2. In this paper, we study optimal ternary LRCs meeting this Singleton-like bound by employing a parity-check matrix approach. It...
In distributed storage systems, locally repairable codes (LRCs) are introduced to realize low disk I/O and repair cost. In order to tolerate multiple node failures, the LRCs with (r, δ)-localitty are further proposed. Since hot data is not uncommon in a distributed storage system, both Zeh et al. and Kadhe et al. focus on the LRCs with multiple localities or unequal localities (ML-LRCs) recently,...
Recently linear codes with locality properties have attracted a lot of interest due to their desirable applications in distributed storage systems. An [n, k, d] linear code with (r, δ)-locality can enable the local recovery of a failed node in case of more than one node failures. In this paper, we study the theoretical bounds and constructions of linear codes with (r, δ)-locality for all code symbols...
In distributed storage systems, locally repairable codes (LRCs) have attracted lots of interest recently. If a code symbol can be repaired respectively by $t$ disjoint groups of other symbols, each of which has size at most $r$, we say that the code symbol has $(r,t) $-locality. LDPC codes are linear block codes defined by low-density parity-check matrices. A regular $(\tau,\rho)$-LDPC code has the...
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