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 …

Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …

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 …

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 …

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 …

Locally repairable codes, or locally recoverable codes (LRC for short), are designed for
applications in distributed and cloud storage systems. Similar to classical block codes, there …

Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and
cloud storage systems about nine years ago. A lot of progress on the study of LRCs has …

A code is said to be an r-local locally repairable code (LRC) if each of its coordinates can be
repaired by accessing at most r other coordinates. When some of the r coordinates are also …

In this paper, locally repairable codes which have optimal minimum Hamming distance with
respect to the bound presented by Prakash et al. are considered. New upper bounds on the …