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-tensor code consists of matrices whose columns satisfy ''parity checks and rows satisfy
''parity checks (ie, a tensor code is the tensor product of a column code and row code) …

Partial maximum distance separable (PMDS) codes are a kind of erasure codes where the
nodes are divided into multiple groups with each forming an MDS code with a smaller code …

Locality enables storage systems to recover failed nodes from small subsets of surviving
nodes. The setting where nodes are partitioned into subsets, each allowing for local …

We establish a connection between problems studied in rigidity theory and matroids arising
from linear algebraic constructions like tensor products and symmetric products. A special …

In recent years, the rapidly increasing amounts of data created and processed through the
internet resulted in distributed storage systems employing erasure coding based schemes …

Product codes are a class of codes which have generator matrices as the tensor product of
the component codes and the codeword itself can be represented as an (m× n) array, where …

In the field of coding theory, maximum-distance separable (MDS) codes are a class of codes
which have optimal guarantees for correcting worst-case Hamming errors. Geometrically …

This work investigates different concepts related distributed storage, starting from codes with
locality properties, such as maximally recoverable codes for grid-like topologies …