Linear exact repair schemes for free MDS and Reed-Solomon codes over Galois rings

TL;DR

This paper develops linear exact repair schemes for free MDS and Reed-Solomon codes over Galois rings, enhancing data recovery efficiency in distributed storage systems.

Contribution

It introduces a novel linear repair scheme specifically for free MDS codes and full-length Reed-Solomon codes over Galois rings, extending existing repair methods.

Findings

Provides a linear repair scheme for free MDS codes over Galois rings.

Develops a repair scheme for full-length Reed-Solomon codes over Galois rings.

Enhances data recovery efficiency in distributed storage systems.

Abstract

Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed storage system uses a linear code to encode a large file across several nodes. If one of the nodes fails, a linear exact repair scheme efficiently recovers the failed node by accessing and downloading data from the rest of the servers of the storage system. In this article, we develop a linear repair scheme for free maximum distance separable codes, which coincide with free maximum distance with respect to the rank codes over Galois rings. In particular, we give a linear repair scheme for full-length Reed-Solomon codes over a Galois ring.