2023/04/24 by Elisa Gorla, Umberto Martínez-Peñas, Gorla, Elisa +3 · 1 citation
Computer Science · Engineering · #Advanced Wireless Communication Technologies #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Networks Research
paper · pdf · doi:10.48550/arxiv.2304.12095
openalex publication_date 2023/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Sum-rank metric codes are a natural extension of both linear block codes and rank-metric codes. They have several applications in information theory, including multishot network coding and distributed storage systems. The aim of this chapter is to present the mathematical theory of sum-rank metric codes, paying special attention to the \mathbbFq-linear case in which different sizes of matrices are allowed. We provide a comprehensive overview of the main results in the area. In particular, we discuss invariants, optimal anticodes, and MSRD codes. In the last section, we concentrate on \mathbbFqm-linear codes.