Locality for Codes over the Integers

In this work, we study the codes over the integers with locality constraints. We introduce a weighted notion of locality over $\mathbb{Z}\mathrm{/}{q}_1\mathbb{Z}\times \cdots \times \mathbb{Z}\mathrm{/}{q}_n\mathbb{Z}$ 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.