# On One Generalization of LRC Codes with Availability

## TL;DR

This paper explores a generalized class of locally recoverable codes with intersecting recovery sets, enabling higher code rates and load balancing, supported by theoretical bounds and explicit constructions.

## Contribution

It introduces a new generalization of LRC codes with intersecting recovery sets, providing bounds and explicit constructions that improve code rate and load balancing capabilities.

## Key findings

- Derived an upper bound for the code rate.
- Provided explicit constructions of the generalized LRC codes.
- Showed the benefits of intersecting recovery sets in code performance.

## Abstract

We investigate one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable code rate and still meet load balancing requirements. In this paper we derive an upper bound for the rate of such codes and give explicit constructions of codes with such a property. These constructions utilize LRC codes developed by Wang et al.