Explicit optimal-length locally repairable codes of distance 5

TL;DR

This paper presents explicit constructions of optimal locally repairable codes with minimum distance 5, achieving the best possible length relative to the alphabet size, which enhances data storage robustness.

Contribution

It provides the first explicit constructions of optimal-length LRCs with distance 5, expanding the known code parameters for data reliability.

Findings

Constructed explicit optimal LRCs with distance 5

Achieved polynomial bounds on code length relative to alphabet size

Enhanced robustness in data storage systems

Abstract

Locally repairable codes (LRCs) have received significant recent attention as a method of designing data storage systems robust to server failure. Optimal LRCs offer the ideal trade-off between minimum distance and locality, a measure of the cost of repairing a single codeword symbol. For optimal LRCs with minimum distance greater than or equal to 5, block length is bounded by a polynomial function of alphabet size. In this paper, we give explicit constructions of optimal-length (in terms of alphabet size), optimal LRCs with minimum distance equal to 5.