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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


D. Thompson


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.

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 Oct 21, 2023
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
Keywords Skew polynomial ring; skew polynomials; division algebras; MRD codes
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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 (, 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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