Locally Recoverable codes from algebraic curves with separated variables

TL;DR

This paper explores Locally Recoverable Algebraic Geometry codes derived from specific algebraic curves, demonstrating efficient erasure recovery methods including Lagrangian interpolation and simple addition.

Contribution

It introduces a new class of LRC codes from algebraic curves with separated variables, providing novel recovery techniques and analysis.

Findings

Recovery via Lagrangian interpolation

Simple addition suffices in special cases

Enhanced understanding of algebraic geometry codes

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. We study Locally Recoverable Algebraic Geometry codes arising from certain curves defined by equations with separated variables. The recovery of erasures is obtained by means of Lagrangian interpolation in general, and simply by one addition in some particular cases.