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Division algebras and MRD codes from skew polynomials

Thompson, D.; Pumplün, S.

Division algebras and MRD codes from skew polynomials Thumbnail


Authors

D. Thompson



Abstract

Let be a division algebra, finite-dimensional over its center, and a skew polynomial ring. Using skew polynomials, we construct division algebras and maximum rank distance codes consisting of matrices with entries in a noncommutative division algebra or field. These include Jha Johnson semifields, and the classes of classical and twisted Gabidulin codes constructed by Sheekey.

Citation

Thompson, D., & Pumplün, S. (2023). Division algebras and MRD codes from skew polynomials. Glasgow Mathematical Journal, 65(2), 480-500. https://doi.org/10.1017/S001708952300006X

Journal Article Type Article
Acceptance Date Feb 28, 2023
Online Publication Date Apr 20, 2023
Publication Date 2023-05
Deposit Date Feb 28, 2023
Publicly Available Date Mar 29, 2024
Journal Glasgow Mathematical Journal
Print ISSN 0017-0895
Electronic ISSN 1469-509X
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 65
Issue 2
Pages 480-500
DOI https://doi.org/10.1017/S001708952300006X
Keywords Skew polynomial ring; skew polynomials; division algebras; MRD codes
Public URL https://nottingham-repository.worktribe.com/output/17938098
Publisher URL https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/division-algebras-and-mrd-codes-from-skew-polynomials/DDB038779765ED0C4C06178B0FF7EF4C
Additional Information Copyright: © The Author(s), 2023. Published by Cambridge University Press in association with Glasgow Mathematical Journal Trust; License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.; Free to read: This content has been made available to all.

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