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

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


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