Sum-rank metric codes
Information Theory
2023-04-25 v1 math.IT
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 -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 -linear codes.
Cite
@article{arxiv.2304.12095,
title = {Sum-rank metric codes},
author = {Elisa Gorla and Umberto Martínez-Peñas and Flavio Salizzoni},
journal= {arXiv preprint arXiv:2304.12095},
year = {2023}
}