# Repair Duality with Locally Repairable and Locally Regenerating Codes

## TL;DR

This paper introduces an explicit family of locally repairable and regenerating codes based on HashTag codes, demonstrating their construction, field size reduction, and the practical advantages of dual repair methods in distributed storage systems.

## Contribution

The paper provides the first explicit construction of locally repairable and regenerating codes with dual repair options, based on HashTag codes, and discusses their practical benefits.

## Key findings

- Explicit code construction based on HashTag codes.
- Reduced finite field size requirements.
- Practical benefits demonstrated in Hadoop experiments.

## Abstract

We construct an explicit family of locally repairable and locally regenerating codes whose existence was proven in a recent work by Kamath et al. about codes with local regeneration but no explicit construction was given. This explicit family of codes is based on HashTag codes. HashTag codes are recently defined vector codes with different vector length $\alpha$ (also called a sub-packetization level) that achieve the optimal repair bandwidth of MSR codes or near-optimal repair bandwidth depending on the sub-packetization level. We applied the technique of parity-splitting code construction. We show that the lower bound on the size of the finite field for the presented explicit code constructions can be lower than the one given in the work of Kamath et al. Finally, we discuss the importance of having two ways for node repair with locally regenerating HashTag codes: repair only with local parity nodes or repair with both local and global parity nodes. To the best of the authors' knowledge, this is the first work where this duality in repair process is discussed. We give a practical example and experimental results in Hadoop where we show the benefits of having this repair duality.