Rank-Metric Codes and Their Applications

ISBN-13: 9781638280002 / Angielski / Miękka / 2022 / 172 str.

Antonia Wachter-Zeh;Hannes Bartz;Hedongliang Liu

Opis

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.

Spis treści

• 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