# Matroid Theory and Storage Codes: Bounds and Constructions

## TL;DR

This paper explores the relationship between matroid theory and distributed storage codes, introducing matroids and polymatroids, and illustrating their relevance to locally repairable codes with bounds and examples.

## Contribution

It provides an accessible introduction to matroids in the context of storage codes, connecting theoretical concepts with practical bounds and code features.

## Key findings

- Matroid theory offers a framework for understanding storage code properties.
- The chapter presents generalized Singleton bounds for locally repairable codes.
- Examples demonstrate the application of matroids to code design.

## Abstract

Recent research on distributed storage systems (DSSs) has revealed interesting connections between matroid theory and locally repairable codes (LRCs). The goal of this chapter is to introduce the reader to matroids and polymatroids, and illustrate their relation to distribute storage systems. While many of the results are rather technical in nature, effort is made to increase accessibility via simple examples. The chapter embeds all the essential features of LRCs, namely locality, availability, and hierarchy alongside with related generalised Singleton bounds.