Can I read On the List-Decodability of Random (Linear) Sum-Rank Metric Codes on EtoBox?

On the List-Decodability of Random (Linear) Sum-Rank Metric Codes by Liu, Yang; Baumeister, Anna; Wachter-Zeh, Antonia is a scholarly article available to read on EtoBox.

What is On the List-Decodability of Random (Linear) Sum-Rank Metric Codes about?

In this paper, we establish the list-decoding capacity theorem for sum-rank metric codes. This theorem implies the list-decodability theorem for random general sum-rank metric codes: Any random general sum-rank metric code with a rate not exceeding the list-decoding capacity is $\left(\rho,O\left(1/\epsilon\right)\right)$-list-decodable with high probability, where $\rho\in\left(0,1\right)$ represents the error fraction and $\epsilon>0$ is referred to as the capacity gap. For random $\mathbb{F}_q$-linear sum-rank metric codes by using the same proof approach we demonstrate that any random $\mathbb{F}_q$-linear sum-rank metric code with a rate not exceeding the list-decoding capacity is $\left(\rho,\exp\left(O\left(1/\epsilon\right)\right)\right)$-list-decodable with high probability, where the list size is exponential at this stage due to the high correlation among codewords in linear codes. To achieve an exponential improvement on the list size, we prove a limited correlation property between sum-rank metric balls and $\mathbb{F}_q$-subspaces. Ultimately, we establish the list-decodability theorem for random $\mathbb{F}_q$-linear sum-rank metric codes: Any random $\mathbb{F}_q$-li

Author

Liu, Yang; Baumeister, Anna; Wachter-Zeh, Antonia

Published

2025

Language

EN