In this work, we study the codes over the integers with locality constraints. We introduce a weighted notion of locality over $\mathbb{Z}/q_1\mathbb{Z} \times \cdots \times \mathbb{Z}/q_n\mathbb{Z}$ 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.

翻译：本文研究了具有局域性约束的整数环上码。我们提出了在积环$\mathbb{Z}/q_1\mathbb{Z} \times \cdots \times \mathbb{Z}/q_n\mathbb{Z}$上加权的局域性概念，并推导了局部可恢复码的Singleton类界。此外，我们给出了若干具有局域性的码构造，包括Tamo-Barg码的整数类比。