Rank-Metric Codes and Their Applications

TL;DR

This survey introduces rank-metric codes, explaining their fundamental properties and highlighting their diverse applications in network coding, cryptography, distributed storage, and caching.

Contribution

It provides a comprehensive overview of rank-metric codes, emphasizing their significance and recent developments across multiple application domains.

Findings

Rank-metric codes are crucial in network coding and cryptography.

They enable efficient data storage and retrieval in distributed systems.

Applications include reducing public-key sizes and improving data locality.

Abstract

The rank metric measures the distance between two matrices by the rank of their difference. Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a variety of applications. In code-based cryptography, the hardness of the corresponding generic decoding problem can lead to systems with reduced public-key size. In distributed data storage, codes in the rank metric have been used repeatedly to construct codes with locality, and in coded caching, they have been employed for the placement of coded symbols. This survey gives a general introduction to rank-metric codes, explains their most important applications, and highlights their relevance to these areas of research.