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

Susanne Pumplün

doi:10.3934/amc.2014.8.323

Article Contents

2014, Volume 8, Issue 3: 323-342. Doi: 10.3934/amc.2014.8.323

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

Susanne Pumplün^1,

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

Received: July 2013

Revised: March 2014

Published: August 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 17A35, 94B05.

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