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 …

A code over a finite alphabet is called locally recoverable (LRC) if every symbol in the
encoding is a function of a small number (at most r) other symbols. We present a family of …

An (n, k, l) maximum distance separable (MDS) array code of length n, dimension k= nr, and
subpacketization l is formed of l× n matrices over a finite field F, with every column of the …

A locally repairable code (LRC) with locality r allows for the recovery of any erased
codeword symbol using only r other codeword symbols. A Singleton-type bound dictates the …

In distributed storage systems, erasure codes with locality r are preferred because a
coordinate can be locally repaired by accessing at most r other coordinates which in turn …

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 …

Like classical block codes, a locally repairable code also obeys the Singleton-type bound
(we call a locally repairable code optimal if it achieves the Singleton-type bound). In the …

Constructing locally repairable codes achieving Singleton-type bound (we call them optimal
codes in this paper) is a challenging task and has attracted great attention in the last few …

A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the
encoding is a function of a small number (at most r) of other symbols of the codeword. In this …

Codes for storage systems aim to minimize the repair locality, which is the number of disks
(or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must …