In this work, we study the codes over the integers with locality constraints. We introduce a weighted notion of locality over Z/q1Z×⋯×Z/qnZ and derive a Singleton-like bound for locally recoverable codes. We also propose some code constructions with locality, including integer analogs of Tamo--Barg codes.
@article{arxiv.2604.26756,
title = {Locality for Codes over the Integers},
author = {Giulia Cavicchioni and Eleonora Guerrini and Julien Lavauzelle},
journal= {arXiv preprint arXiv:2604.26756},
year = {2026}
}