# Construction of Binary Locally Repairable Codes with Nonuniform Locality and Availability Using Combinatorial Designs

## TL;DR

This paper introduces new binary codes for efficient data repair using combinatorial designs, offering better performance and flexibility.

## Contribution

The paper proposes novel binary LRC constructions with nonuniform locality and availability using combinatorial designs.

## Key findings

- Binary LRCs with nonuniform localities and (r,t)-availability are constructed using PBDs and BIBDs.
- The codes achieve optimal minimum distance and higher code rates compared to existing methods.
- The constructions solve open problems where r does not divide k and generalize prior works.

## Abstract

In this paper, we generalize the construction of locally repairable codes (LRCs) by leveraging pairwise balanced designs (PBDs) and balanced incomplete block designs (BIBDs) to construct codes with nonuniform locality or nonuniform availability. Our constructions prioritize binary implementations for practical deployment while achieving optimal or near-optimal performance in terms of rate, minimum distance, and repair efficiency. Specifically, we propose distance-optimal LRCs with nonuniform localities and message-symbol (r,t)-availability. These binary constructions achieve optimal minimum distance under known bounds and have higher code rates than existing works. We also address open problems in the literature, including constructions where r∤k, and demonstrate that our constructions encompass or outperform several prior works.