Division algebras and MRD codes from skew polynomials
Rings and Algebras
2023-03-02 v2
Abstract
Let be a division algebra, finite-dimensional over its center, and a skew polynomial ring. Using skew polynomials , we construct division algebras and a generalization of maximum rank distance codes consisting of matrices with entries in a noncommutative division algebra or field. These include a class of codes constructed by Sheekey (in particular, generalized Gabidulin codes), as well as Jha Johnson semifields.
Cite
@article{arxiv.2103.12691,
title = {Division algebras and MRD codes from skew polynomials},
author = {Daniel Thompson and Susanne Pumpluen},
journal= {arXiv preprint arXiv:2103.12691},
year = {2023}
}