The book "Rank Codes" by Ernst Gabidulin
The book was prepared for publication (translated to English and edited) by the Institute for Communications Engineering, Technical University of Munich, and will be published May, 3, 2021 by TUM.University Press.
Apr 28, 2021
The book "Rank Codes" by E. Gabidulin

This textbook contains the theory and some applications of the rank metric codes developed by the author and called Gabidulin Codes by the scientific community. A matrix code C is a set of matrices (codewords) of fixed size over a finite field. The code is considered in the rank metric that is defined as follows: The distance between two matrices is the rank of their difference. The code distance of a code C is the minimum distance between different code matrices. Given a metric, the main directions of coding theory are to design codes with a maximum number of codewords for a fixed code distance, to obtain the properties of the codes, and to construct efficient decoding algorithms that find a code matrix nearest to a given matrix. This book can be recommended to students and researchers working with rank metric codes.

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                                                 Gerhard Kramer, Vladimir Sidorenko, Antonia Wachter-Zeh