Research Repository

# Division algebras and MRD codes from skew polynomials

## Authors

Daniel Thompson

### 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 Feb 28, 2023 Feb 28, 2023 Glasgow Mathematical Journal 0017-0895 1469-509X Cambridge University Press Peer Reviewed https://nottingham-repository.worktribe.com/output/17938098

This file is under embargo due to copyright reasons.