We propose a generic transformation that can convert any nonbinary (n= k+ r, k) maximum
distance separable (MDS) code into another (n, k) MDS code over the same field such that …

The traditional means of ensuring reliability in data storage is to store multiple copies of the
same file in different storage units. Such a replication strategy is clearly inefficient in terms of …

An-vector MDS code over a field is a-linear subspace of of dimension, such that any (vector)
symbols of the codeword suffice to determine the remaining (vector) symbols. The length of …

Erasure codes are essential for providing efficient resilience against node failures in
distributed storage. Typically, an erasure code encodes symbols into symbols which are …

Erasure codes are typically used in large-scale distributed storage systems to provide
durability of data in the face of failures. In this setting, a set of k blocks to be stored is …

An (n, k, ℓ)-vector MDS code is a F-linear subspace of (Fℓ) n (for some field F) of dimension k
ℓ, such that any k (vector) symbols of the codeword suffice to determine the remaining r= n …

Recently, some high-rate maximum distance separable (MDS) array codes were designed
to optimally repair a single failed node by connecting all the surviving nodes. However, in …

We consider (n, k, l) MDS codes of length n, dimension k, and subpacketization l over a finite
field F. A codeword of such a code consists of n column-vectors of length l over F, with the …

In the literature, most of the known high-rate MDS array codes with the optimal repair
property only support a single repair degree (ie, the number of helper nodes contacted …

Many distributed storage systems use erasure codes rather than replication for higher
reliability at significantly lower storage costs. However, using traditional erasure codes …