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Quotients of orders in cyclic algebras and space-time codes

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  • Let $F$ be a number field with ring of integers $\boldsymbol{O}_F$ and $D$ a division $F$-algebra with a maximal cyclic subfield $K$. We study rings occurring as quotients of a natural $\boldsymbol{O}_F$-order $\Lambda$ in $D$ by two-sided ideals. We reduce the problem to studying the ideal structure of $\Lambda/q^s\Lambda$, where $q$ is a prime ideal in $\boldsymbol{O}_F$, $s\geq 1$. We study the case where $q$ remains unramified in $K$, both when $s=1$ and $s>1$. This work is motivated by its applications to space-time coded modulation.
    Mathematics Subject Classification: Primary: 11S45; Secondary: 11T71, 94B40.

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