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Constructions of Optimal (r,δ) Locally Repairable Codes via Constacyclic Codes
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Locally repairable codes (LRCs) are introduced in distributed storage systems due to their low repair overhead. An LRC is called optimal if its minimum distance attains the Singleton-like upper bound. Chen et al. (2018) recently studied the constructions...

Optimal Constacyclic Locally Repairable Codes
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Being part of distributed storage systems, locally repairable codes (LRCs) have drawn great attention in the past years. Inspired by a recent construction of optimal LRCs based on cyclic codes, constacyclic LRCs are studied in this...

Optimal constacyclic locally repairable codes
2019 Edition, Volume 23, February 1, 2019 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Being part of distributed storage systems, locally repairable codes (LRCs) have drawn great attention in the past years. Inspired by a recent construction of optimal LRCs-based on cyclic codes, constacyclic LRCs are studied in this...

On the Combinatorics of Locally Repairable Codes via Matroid Theory
2016 Edition, Volume 62, October 1, 2016 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

This paper provides a link between matroid theory and locally repairable codes (LRCs) that are either linear or more generally almost affine. Using this link, new results on both LRCs and matroid theory are derived. The parameters (n, k, d, r, δ) of LRCs...

On Optimal (r, δ)-LRCs with Length n | (q+1)
2018 Edition, November 1, 2018 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Optimal (r, δ) locally repairable codes ((r, δ)-LRCs for short) with length n | (q+1) have been studied in [5] and [6]. In this paper, along with their ideas, by using cyclic or constacyclic codes, we construct three classes...

Constructions of Optimal Cyclic (r,δ) Locally Repairable Codes
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

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 erased, the r-local LRC can not...

Complete Characterizations of Optimal Locally Repairable Codes with Locality 1 and k – 1
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

locally repairable code (LRC) is a [n, k, d] linear code with length n, dimension k, minimum distance d and locality r, which means that every code symbol can be repaired by at most r other symbols. LRCs have become an important candidate in...

New Optimal Cyclic Locally Recoverable Codes of Length n=2(q+1)
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Locally recoverable codes are very important due to their applications in distributed storage systems. In this paper, by using cyclic codes, we construct two classes of optimal q-ary cyclic (r,δ1) locally recoverable codes with parameters...

Classification of Optimal Ternary (r, δ)-Locally Repairable Codes Attaining the Singleton-like Bound
2019 Edition, July 1, 2019 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

In a linear code, a code symbol with (r, δ)-locality can be repaired by accessing at most r other code symbols in case of at most δ − 1 erasures. A q-ary (n, k, r, δ) locally repairable codes (LRC) in...

Optimal Locally Repairable Linear Codes
2014 Edition, Volume 32, May 1, 2014 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n, k, d] linear code having all-symbol (r, δ)-locality, denoted as (r, δ)a, is considered optimal if it has the actual highest minimum...

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