Foundations and Trends® in Communications and Information Theory > Vol 19 > Issue 3

Rank-Metric Codes and Their Applications

By Hannes Bartz, German Aerospace Center (DLR), Germany, hannes.bartz@dlr.de | Lukas Holzbaur, Technical University of Munich, Germany, lukas.holzbaur@tum.de | Hedongliang Liu, Technical University of Munich, Germany, lia.liu@tum.de | Sven Puchinger, Hensoldt Sensors GmbH, Germany, mail@svenpuchinger.de | Julian Renner, Technical University of Munich, Germany, julian.renner@tum.de | Antonia Wachter-Zeh, Technical University of Munich, Germany, antonia.wachter-zeh@tum.de

 
Suggested Citation
Hannes Bartz, Lukas Holzbaur, Hedongliang Liu, Sven Puchinger, Julian Renner and Antonia Wachter-Zeh (2022), "Rank-Metric Codes and Their Applications", Foundations and TrendsĀ® in Communications and Information Theory: Vol. 19: No. 3, pp 390-546. http://dx.doi.org/10.1561/0100000119

Publication Date: 02 May 2022
© 2022 H. Bartz et al.
 
Subjects
Coding theory and practice,  Information theory and computer science,  Cryptology and data security,  Data networks,  Network Coding
 

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In this article:
1. Introduction
2. Basics on Rank-Metric Codes
3. Applications to Code-Based Cryptosystems
4. Applications to Storage
5. Applications to Network Coding
6. Conclusion
Acknowledgements
References

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.

DOI:10.1561/0100000119
ISBN: 978-1-63828-000-2
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Table of contents:
1. Introduction
2. Basics on Rank-Metric Codes
3. Applications to Code-Based Cryptosystems
4. Applications to Storage
5. Applications to Network Coding
6. Conclusion
Acknowledgements
References

Rank-Metric Codes and Their Applications

Rank-metric codes date back to the 1970s and today play a vital role in many areas of coding theory and cryptography. In this survey the authors provide a comprehensive overview of the known properties of rank-metric codes and their applications.

The authors begin with an accessible and complete introduction to rank-metric codes, their properties and their decoding. They then discuss at length rank-metric code-based quantum resistant encryption and authentication schemes. The application of rank-metric codes to distributed data storage is also outlined. Finally, the constructions of network codes based on MRD codes, constructions of subspace codes by lifting rank-metric codes, bounds on the cardinality, and the list decoding capability of subspace codes is covered in depth.

Rank-Metric Codes and Their Applications provides the reader with a concise, yet complete, general introduction to rank-metric codes, explains their most important applications, and highlights their relevance to these areas of research.

 
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