# Computing sharp recovery structures for Locally Recoverable codes

## TL;DR

This paper presents an algorithm to compute optimal recovery structures for any linear code, enhancing local recoverability and providing insights into code locality and dual distance, with complexity analysis and examples.

## Contribution

It introduces a novel algorithm that efficiently finds the most concise recovery structures for linear codes, advancing the design of locally recoverable codes.

## Key findings

- Algorithm computes minimal recovery structures
- Provides locality and dual distance of codes
- Includes complexity analysis and practical examples

## Abstract

A locally recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. In this article we develop an algorithm that computes a recovery structure as concise posible for an arbitrary linear code $\mathcal{C}$ and a recovery method that realizes it. This algorithm also provides the locality and the dual distance of $\mathcal{C}$. Complexity issues are studied as well. Several examples are included.