# An Explicit, Coupled-Layer Construction of a High-Rate Regenerating Code with Low Sub-Packetization Level, Small Field Size and $d< (n-1)$

## TL;DR

This paper introduces an explicit construction of high-rate regenerating codes with low sub-packetization, small field size, and flexible parameters, improving efficiency and repair capabilities in distributed storage systems.

## Contribution

It provides a novel explicit code construction achieving high rate, low sub-packetization, and uniform repair bandwidth, with parameters close to optimal and manageable field size.

## Key findings

- Achieves rate close to 1 with explicit construction.
- Maintains low sub-packetization level for practical implementation.
- Ensures all code symbols can be repaired with minimal data download.

## Abstract

This paper presents an explicit construction for an $((n=2qt,k=2q(t-1),d=n-(q+1)), (\alpha = q(2q)^{t-1},\beta = \frac{\alpha}{q}))$ regenerating code (RGC) over a field $\mathbb{F}_Q$ having rate $\geq \frac{t-2}{t}$. The RGC code can be constructed to have rate $k/n$ as close to $1$ as desired, sub-packetization level $\alpha \leq r^{\frac{n}{r}}$ for $r=(n-k)$, field size $Q$ no larger than $n$ and where all code symbols can be repaired with the same minimum data download.