# Array Codes with Local Properties

## TL;DR

This paper introduces enhanced array codes with added column parity, enabling local symbol recovery, which improves data repair efficiency in RAID-like storage systems.

## Contribution

The paper extends traditional array codes by incorporating column parity, facilitating local recovery and advancing the design of locally recoverable codes.

## Key findings

- Added column parity enables local symbol recovery.
- Enhanced codes maintain array code properties with improved repair.
- Applications to Locally Recoverable (LRC) codes are discussed.

## Abstract

In general, array codes consist of $m\times n$ arrays and in many cases, the arrays satisfy parity constraints along lines of different slopes (generally with a toroidal topology). Such codes are useful for RAID type of architectures, since they allow to replace finite field operations by XORs. We present expansions to traditional array codes of this type, like Blaum-Roth (BR) and extended EVENODD codes, by adding parity on columns. This vertical parity allows for recovery of one or more symbols in a column locally, i.e., by using the remaining symbols in the column without invoking the rest of the array. Properties and applications of the new codes are discussed, in particular to Locally Recoverable (LRC) codes.