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arXiv · 1210.7044

Quotients of Orders in Cyclic Algebras and Space-Time Codes

Frederique Oggier·B. A. Sethuraman
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Abstract

Let $F$ be a number field with ring of integers $\Oc_F$ and $\Dc$ a division $F$-algebra with a maximal cyclic subfield $K$. We study rings occurring as quotients of a natural $\Oc_F$-order $Λ$ in $\Dc$ by two-sided ideals. We reduce the problem to studying the ideal structure of $Λ/\qf^sΛ$, where $\qf$ is a prime ideal in $\Oc_F$, $s\geq 1$. We study the case where $\qf$ remains unramified in $K$, both when $s=1$ and $s>1$. This work is motivated by its applications to space-time coded modulation.

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Frederique Oggier, B. A. Sethuraman. 2012-10-26. Quotients of Orders in Cyclic Algebras and Space-Time Codes. https://arxiv.org/abs/1210.7044

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