Skip to main content

Research Repository

Advanced Search

Division algebras and MRD codes from skew polynomials

Thompson, Daniel; Pumpluen, Susanne


Daniel Thompson


Let $D$ be a division algebra, finite-dimensional over its center, and $R=D[t;\sigma,\delta]$ a skew polynomial ring.

Using skew polynomials $f\in R$, 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.


Thompson, D., & Pumpluen, S. (in press). Division algebras and MRD codes from skew polynomials. Glasgow Mathematical Journal,

Journal Article Type Article
Acceptance Date Feb 28, 2023
Deposit Date Feb 28, 2023
Journal Glasgow Mathematical Journal
Print ISSN 0017-0895
Electronic ISSN 1469-509X
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Public URL