# American Institute of Mathematical Sciences

August  2014, 8(3): 323-342. doi: 10.3934/amc.2014.8.323

## How to obtain division algebras used for fast-decodable space-time block codes

 1 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD

Received  July 2013 Revised  March 2014 Published  August 2014

We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra $D=(K/F,\sigma,c)$, employing a $K$-automorphism $\tau$ and an element $d\in D^\times$. These algebras appear in the construction of iterated space-time block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly look at algebras (and codes) obtained from variations of this method.
Citation: Susanne Pumplün. How to obtain division algebras used for fast-decodable space-time block codes. Advances in Mathematics of Communications, 2014, 8 (3) : 323-342. doi: 10.3934/amc.2014.8.323
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