# A Systematic Construction of MDS Codes With Small Sub-packetization Level and Near-Optimal Repair Bandwidth

## TL;DR

This paper introduces a transformation technique to construct high-rate MDS codes with small sub-packetization levels and near-optimal repair bandwidth, making them more practical for real-world systems.

## Contribution

It presents a novel transformation that reduces sub-packetization levels of MDS codes while maintaining near-optimal repair bandwidth, along with explicit code constructions.

## Key findings

- Four high-rate MDS codes with small sub-packetization and near-optimal repair bandwidth are constructed.
- Three of the codes are explicit with small field sizes, making implementation feasible.
- An additional explicit MDS code is proposed with a smaller finite field requirement.

## Abstract

In the literature, all the known high-rate MDS codes with the optimal repair bandwidth possess a significantly large sub-packetization level, which may prevent the codes to be implemented in practical systems. To build MDS codes with small sub-packetization level, existing constructions and theoretical bounds imply that one may sacrifice the optimality of the repair bandwidth. Partly motivated by the work of Tamo et al. (IEEE Trans. Inform. Theory, 59(3), 1597-1616, 2013), in this paper, we present a transformation that can greatly reduce the sub-packetization level of MDS codes with the optimal repair bandwidth with respect to the same code length n. As applications of the transformation, four high-rate MDS codes having both small sub-packetization level and near-optimal repair bandwidth can be obtained, where three of them are explicit and the required field sizes are around or even smaller than the code length n. Additionally, we propose another explicit MDS code which has a similar structure as that of the first resultant code obtained by the generic transformation, but can be built on a smaller finite field.