Codes in the Sum-Rank Metric: Fundamentals and Applications Martnez-Peas Umberto
Codes in the Sum-Rank Metric: Fundamentals and Applications Martnez-Peas Umberto Hamming distance and rank metric have long been used in coding theory. They have attracted significant attention for…
Specifikacia Codes in the Sum-Rank Metric: Fundamentals and Applications Martnez-Peas Umberto
Codes in the Sum-Rank Metric: Fundamentals and Applications Martnez-Peas Umberto
Hamming distance and rank metric have long been used in coding theory. They have attracted significant attention for their applications in distributed storage systems, multishot network coding, streaming over erasure channels, and multi-antenna wireless communication. The sum-rank metric naturally extends these over fields.
At the heart of the monograph is the construction of linearized Reed-Solomon codes, a general construction of maximum sum-rank distance (MSRD) codes with polynomial field sizes. In this monograph, the authors provide a tutorial introduction to the theory and applications of sum-rank metric codes over finite fields. These specialize to classical Reed-Solomon and Gabidulin code constructions in the Hamming and rank metrics, respectively and produce an efficient Welch-Berlekamp decoding algorithm.
The authors proceed to develop applications of these codes in distributed