Division algebras and MRD codes from skew polynomials

Thompson, Daniel; Pumpluen, Susanne

Abstract

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.

Citation

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: https://nottingham-repository.worktribe.com/output/17938098