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arXiv · 2304.12095

Sum-rank metric codes

Elisa Gorla·Umberto Martínez-Peñas·Flavio Salizzoni
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Abstract

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 $\mathbb{F}_q$-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 $\mathbb{F}_{q^m}$-linear codes.

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Elisa Gorla, Umberto Martínez-Peñas, Flavio Salizzoni. 2023-04-24. Sum-rank metric codes. https://arxiv.org/abs/2304.12095

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