A Construction of Optimal $(r,\delta)$ -Locally Recoverable Codes

Bocong Chen,Jing Huang

doi:10.1109/access.2019.2957942

Abstract

Locally recoverable codes (LRCs) play a significant role in distributed and cloud storage systems. The key ingredient for constructing such optimal LRCs is to characterize the parity-check matrix for LRCs. In this letter based on the parity-check matrix for generalized Reed-Solomon codes we mainly present new constructions of optimal (r, δ)-locally recoverable codes with unbounded lengths in terms of the properties of the Vandermonde matrices, of which the parameters contain the known ones.

Highlights

In the application of distributed storage, locally recoverable codes (LRCs for convenience) with locality r are used to design for the failed storage nodes, which was put forward by Gopalan et al [3]
For increasing the chances of successful recover, Prakash et al [4] proposed the concept of locally recoverable codes with locality (r, δ), which generalizes the notion of locally recoverable codes with locality r
In this letter, motivated by the above works, we construct a class of new optimal (r, δ)-Locally recoverable codes (LRCs) with unbounded lengths via generalized Reed-Solomon codes (GRS codes for short), of which the parameters cover the known ones in [1] and [2]

Summary

INTRODUCTION

In the application of distributed storage, locally recoverable codes (LRCs for convenience) with locality r are used to design for the failed storage nodes, which was put forward by Gopalan et al [3]. Chen et al in [5] and [6] constructed some new classes of optimal (r, δ)-LRCs (δ ≥ 2) with lengths n ≤ q + 1 via constacyclic MDS codes (include cyclic MDS codes). In [1], Fang and Fu constructed four families of optimal (r, δ)-LRCs with unbounded lengths through cyclic codes. In this letter, motivated by the above works, we construct a class of new optimal (r, δ)-LRCs with unbounded lengths via generalized Reed-Solomon codes (GRS codes for short), of which the parameters cover the known ones in [1] and [2].

PRELIMINARIES

CONSTRUCTIONS

COROLLARIES AND CODE COMPARISONS

CONCLUSION