Locality for Codes over the Integers
arXiv:2604.2675652.0
AI Analysis
It extends the theory of locally recoverable codes to a new algebraic setting (integer rings), which is incremental for coding theory researchers.
The paper introduces a weighted notion of locality for codes over integer rings and derives a Singleton-like bound for locally recoverable codes, along with constructions including integer analogs of Tamo-Barg codes.
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.