A construction of maximally recoverable codes

TL;DR

This paper introduces a new family of linear maximally recoverable codes with improved parameters, enhancing code efficiency for data recovery in distributed storage systems.

Contribution

It presents a novel construction of maximally recoverable codes with locality and dimension parameters, achieving better alphabet size bounds than previous methods.

Findings

Codes have locality r and dimension r+1.

For code length n and r≈n^α, alphabet size is about n^{1+3α}.

Improves upon previous constructions in terms of alphabet size.

Abstract

We construct a family of linear maximally recoverable codes with locality $r$ and dimension $r+1.$ For codes of length $n$ with $r\approx n^\alpha, 0\le\alpha\le 1$ the code alphabet is of the order $n^{1+3\alpha},$ which improves upon the previously known constructions of maximally recoverable codes.