Locality for Codes over the Integers
Giulia Cavicchioni, Eleonora Guerrini, Julien Lavauzelle

TL;DR
This paper investigates integer-based codes with locality constraints, introducing a weighted locality concept and deriving bounds, along with proposing new code constructions including integer analogs of Tamo--Barg codes.
Contribution
It introduces a weighted locality notion for codes over product rings, establishes a Singleton-like bound, and constructs new codes with locality, including integer analogs of known codes.
Findings
Derived a Singleton-like bound for locally recoverable codes over rings.
Proposed new code constructions with locality, including integer analogs of Tamo--Barg codes.
Extended the concept of locality to weighted notions over product rings.
Abstract
In this work, we study the codes over the integers with locality constraints. We introduce a weighted notion of locality over 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.
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