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1 results

Division algebras and MRD codes from skew polynomials
Part of
- Rings and algebras arising under various constructions
D. Thompson, S. Pumplün
Journal:

Glasgow Mathematical Journal / Volume 65 / Issue 2 / May 2023

Published online by Cambridge University Press:

20 April 2023, pp. 480-500

Print publication:

May 2023
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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.