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arXiv · 2103.12691

Division algebras and MRD codes from skew polynomials

Daniel Thompson·Susanne Pumpluen
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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 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.

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Daniel Thompson, Susanne Pumpluen. 2021-03-23. Division algebras and MRD codes from skew polynomials. https://arxiv.org/abs/2103.12691

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