# Locally recoverable codes from algebraic curves and surfaces

## TL;DR

This paper introduces new constructions of locally recoverable codes derived from algebraic curves and surfaces, enhancing data recovery efficiency in distributed storage systems.

## Contribution

It extends previous work by Barg, Tamo, and Vlut, providing novel algebraic geometric methods for constructing locally recoverable codes.

## Key findings

- Multiple new code constructions from algebraic curves and surfaces
- Improved parameters for local recoverability and code rate
- Enhanced understanding of algebraic geometric approaches in coding theory

## Abstract

A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. Building on work of Barg, Tamo, and Vl\u{a}du\c{t}, we present several constructions of locally recoverable codes from algebraic curves and surfaces.