Related papers: Optimal $(2,\delta)$ Locally Repairable Codes via …
We study the problem of centralized exact repair of multiple failures in distributed storage. We describe constructions that achieve a new set of interior points under exact repair. The constructions build upon the layered code construction…
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…
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A.…
Like classical block codes, a locally repairable code also obeys the Singleton-type bound (we call a locally repairable code {\it optimal} if it achieves the Singleton-type bound). In the breakthrough work of \cite{TB14}, several classes of…
An [n, k] linear code C that is subject to locality constraints imposed by a parity check matrix H0 is said to be a maximally recoverable (MR) code if it can recover from any erasure pattern that some k-dimensional subcode of the null space…
In this work codes with availability are constructed based on the cyclic \emph{locally repairable code} (LRC) construction by Tamo et al. and their extension to $(r,\rho)$-locality by Chen et al. The minimum distance of these codes is…
Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems. This paper investigates a generalization of the usual locally…
Motivated by the construction of optimal locally repairable codes, we introduce the new finite geometric concept of a \emph{local arc} which is defined as a collection $\mathcal{S}$ of disjoint point sets $S_{i}$ in $\mathrm{PG}(2,q)$ such…
Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory…
Maximally recoverable local reconstruction codes (MR LRCs for short) have received great attention in the last few years. Various constructions have been proposed in literatures. The main focus of this topic is to construct MR LRCs over…
Random linear codes (RLCs) are well known to have nice combinatorial properties and near-optimal parameters in many different settings. However, getting explicit constructions matching the parameters of RLCs is challenging, and RLCs are…
The puncturing and shortening technique are two important approaches to constructing new linear codes from old ones. In the past 70 years, a lot of progress on the puncturing technique has been made, and many works on punctured linear codes…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
In classical coding theory, it is common to construct new codes via propagation rules. There are various propagation rules to construct classical block codes. However, propagation rules have not been extensively explored for constructions…
Error-correcting codes are essential for ensuring fault tolerance in modern distributed data storage systems. However, in practice, factors such as the failure rates of storage devices can vary significantly over time, resulting in changes…
Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…
A locally recoverable code (LRC code) is a code over a finite alphabet such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set. Bounds on the rate and distance of such codes have…
Maximum distance separable (MDS) codes have the optimal trade-off between storage efficiency and fault tolerance, which are widely used in distributed storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can achieve…
Sum-rank-metric codes have wide applications in universal error correction, multishot network coding, space-time coding and the construction of partial-MDS codes for repair in distributed storage. Fundamental properties of sum-rank-metric…
Locally repairable codes have been investigated extensively in recent years due to practical applications in distributed and cloud storage systems. However, there are few asymptotical constructions of locally repairable codes in the…