Related papers: Partial-MDS Codes and their Application to RAID Ty…
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of…
MDS array codes are widely used in storage systems to protect data against erasures. We address the \emph{rebuilding ratio} problem, namely, in the case of erasures, what is the fraction of the remaining information that needs to be…
Large disk arrays are organized into storage nodes -- SNs or bricks with their own cashed RAID controller for multiple disks. Erasure coding at SN level is attained via parity or Reed-Solomon codes. Hierarchical RAID -- HRAID -- provides an…
The continuously increasing amount of digital data generated by today's society asks for better storage solutions. This survey looks at a new generation of coding techniques designed specifically for the needs of distributed networked…
A linear code with parameters $[n,k,n-k]$ is said to be almost maximum distance separable (AMDS for short). An AMDS code whose dual is also AMDS is referred to as an near maximum distance separable (NMDS for short) code. NMDS codes have…
Array codes have been widely employed in storage systems, such as Redundant Arrays of Inexpensive Disks (RAID). The row-diagonal parity (RDP) codes and EVENODD codes are two popular double-parity array codes. As the capacity of hard disks…
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and…
This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the…
Ever-increasing amounts of data are created and processed in internet-scale companies such as Google, Facebook, and Amazon. The efficient storage of such copious amounts of data has thus become a fundamental and acute problem in modern…
As the size of data storing arrays of disks grows, it becomes vital to protect data against double disk failures. A popular method of protection is via the Reed-Solomon (RS) code with two parity words. In the present paper we construct…
New families of maximum distance separable (MDS) codes are constructed from elliptic curves by exploiting their group structures. In contrast to classical constructions based on divisors supported at a single rational point, the proposed…
The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate…
MDS array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with $r$ redundancy nodes can correct any $r$ node erasures by accessing all the remaining information…
Near MDS (NMDS) codes are closely related to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. But there are many unsolved problems about construction of NMDS codes. In this paper, by using…
Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required…
The Big Data trend is putting strain on modern storage systems, which have to support high-performance I/O accesses for the large quantities of data. With the prevalent Von Neumann computing architecture, this data is constantly moved back…
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…
Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given $n$ and $r<n$, with $n$ or $r$ (or both) odd, MDS LCD $(n,r)$ codes are constructed over finite fields whose…
The distributed data storage systems are constructed by large number of nodes which are interconnected over a network. Each node in such peer-to-peer network is vulnerable and at a potential risk for attack. The attackers can eavesdrop the…
Distributed storage systems (DSSs) have gained a lot of interest recently, thanks to their robustness and scalability compared to single-device storage. Majority of the related research has exclusively concerned the network layer. At the…