On Sequential Locally Repairable Codes

On Sequential Locally Repairable Codes Revised by Guangyue.dvi

We consider the locally repairable codes (LRC), aiming at sequentially recovering multiple erasures; in particular, we propose and study the so-called (n, k, r, t)-SLRC (Sequential Locally Repairable Codes) as an [n, k] linear code where any t (≤ t) erasures can be sequentially recovered, each by r (2 ≤ r < k) other code symbols. Here, a sequential recovering means that the erased symbols are r...

Construction of optimal locally repairable codes via automorphism groups of rational function fields

Locally repairable codes, or locally recoverable codes (LRC for short) are designed for application in distributed and cloud storage systems. Similar to classical block codes, there is an important bound called the Singleton-type bound for locally repairable codes. In this paper, an optimal locally repairable code refers to a block code achieving this Singleton-type bound. Like classical MDS co...

On Sequential Locally Repairable Codes - for NVMW 2018.dvi

Optimal Locally Repairable Systematic Codes Based on Packings

Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, we first build a bridge between locally repairable code and packing. As an application of this bridge, some optimal locally repairable codes can be obtained by packings, which gives optimal locally repairable codes with flexible parameters. Index Terms Distributed storage, loc...

Optimal locally repairable codes of distance 3 and 4 via cyclic codes

Like classical block codes, a locally repairable code also obeys the Singleton-type bound (we call a locally repairable code optimal if it achieves the Singleton-type bound). In the breakthrough work of [14], several classes of optimal locally repairable codes were constructed via subcodes of Reed-Solomon codes. Thus, the lengths of the codes given in [14] are upper bounded by the code alphabet...