MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Twisted Linearized Reed-Solomon Codes: A Skew Polynomial Framework

Alessandro Neri


We provide an algebraic description for sum-rank metric codes, as quotient space of a skew polynomial ring. This approach generalizes at the same time the skew group algebra setting for rank-metric codes and the polynomial setting for codes in the Hamming metric. This allows to construct twisted linearized Reed-Solomon codes, a new family of maximum sum-rank distance codes extending at the same time Sheekey's twisted Gabidulin codes in the rank metric and twisted Reed-Solomon codes in the Hamming metric. Furthermore, we provide an analogue in the sum-rank metric of Trombetti-Zhou construction, which also provides a family of maximum sum-rank distance codes. As a byproduct, in the extremal case of the Hamming metric, we obtain a new family of additive MDS codes over quadratic fields.

Jun 8, 2021
Jun 11, 2021
MSC Codes:
16S36, 11T71, 94B05
Sum-rank metric, skew polynomials, twisted linearized Reed-Solomon codes, maximum sum-rank distance codes, MDS codes

Related publications

2022 Repository Open Access
Alessandro Neri

Twisted linearized Reed-Solomon codes : a skew polynomial framework

In: Journal of algebra, 609 (2022), pp. 792-839