A skew polynomial framework for constructing division algebras and linear maximum rank distance codes (opens in new tab)

We construct division algebras and linear maximum rank distance (MRD) matrix codes using skew polynomials over fields. The non-unital division algebras we obtain generalize several prominent constructions: Sheekey's twisted cyclic pre-semifields, i.e. the pre-semifields associated with Jha-Johnson semifields and the semifields associated with Albert's generalized twisted fields. Our linear MRD codes generalize the constructions of Lobillo, Santo...