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.

This book constitutes the proceedings of the 9th International Workshop on Code-Based Cryptography, CBCrypto 2021, which was held during June 21-22, 2021. The workshop was initially planned to take place in Munich, Germany, but changed to an online event due to the COVID-19 pandemic. The 6 papers presented in this volume were carefully reviewed and selected from 14 submissions. These contributions span all aspects of code-based cryptography, from design to implementation, and including studies of security, new systems, and improved decoding algorithms.