In a distributed storage system, code symbols are dispersed across space in nodes or
storage units as opposed to time. In settings such as that of a large data center, an important …

Locally repairable codes (LRCs) are considered with equal or unequal localities, local
distances, and local field sizes. An explicit two-layer architecture with a sum-rank outer code …

Codes in the sum-rank metric have attracted significant attention for their applications in
distributed storage systems, multishot network coding, streaming over erasure channels …

The rank metric measures the distance between two matrices by the rank of their difference.
Codes designed for the rank metric have attracted considerable attention in recent years …

In a paper by Guruswami et al., it was shown that the length n of a q-ary linear locally
recoverable code with distance d≥ 5 is upper bounded by O (dq 3). Thus, it is a challenging …

We construct maximally recoverable codes (corresponding to partial MDS codes) which are
based on linearized Reed-Solomon codes. The new codes have a smaller field size …

We construct six new explicit families of linear maximum sum-rank distance (MSRD) codes,
each of which has the smallest field sizes among all known MSRD codes for some …

Partial MDS (PMDS) codes are a class of erasurecorrecting array codes that combine local
correction of the rows with global correction of the array. An m× n array code is called an (r; …

The explosion in the volumes of data being stored online has resulted in distributed storage
systems transitioning to erasure coding based schemes. Yet, the codes being deployed in …

An-Local Reconstruction Code (LRC) is a linear code over of length, whose codeword
symbols are partitioned into local groups each of size. Each local group satisfies ''local parity …