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Sum-rank metric codes

04/24/2023

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by Elisa Gorla, et al.

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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 𝔽_q-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 𝔽_q^m-linear codes.

Elisa Gorla
15 publications
Umberto Martínez-Peñas
16 publications
Flavio Salizzoni
6 publications

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