Explicit List-Decodable Linearized Reed-Solomon and Folded Linearized Reed-Solomon Subcodes
Kuo Shang, Chen Yuan, Ruiqi Zhu

TL;DR
This paper introduces explicit sum-rank metric codes, including Linearized Reed-Solomon and folded variants, that are efficiently list decodable beyond the unique decoding radius, advancing coding theory in network and cryptography applications.
Contribution
The work constructs explicit sum-rank metric codes with efficient list decoding up to high error fractions, extending LRS codes to folded variants with controlled list sizes.
Findings
Achieved list decoding up to a fraction of errors with rate close to 1-.
Extended decoding framework to folded LRS codes with effective list size control.
First explicit sum-rank codes with efficient list decoding beyond the unique radius.
Abstract
The sum-rank metric is the mixture of the Hamming and rank metrics. The sum-rank metric found its application in network coding, locally repairable codes, space-time coding, and quantum-resistant cryptography. Linearized Reed-Solomon (LRS) codes are the sum-rank analogue of Reed-Solomon codes and strictly generalize both Reed-Solomon and Gabidulin codes. In this work, we construct an explicit family of -linear sum-rank metric codes over arbitrary fields . Our construction enables efficient list decoding up to a fraction of errors in the sum-rank metric with rate , for any desired and . Our codes are subcodes of LRS codes, obtained by restricting message polynomials to an -subspace derived from subspace designs, and the decoding list size is bounded by…
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · Advanced Wireless Communication Techniques
