广义四元数和双四元数代数的二次型和空时分组码
Quadratic Forms and Space-Time Block Codes from Generalized Quaternion and Biquaternion Algebras
摘要：
在空时分组码（STBC）的上下文中，广义四元数和双四元数代数（即，给出了任意基域上两个四元数代数的张量积），以及检验这类代数是否为可除代数的二次型理论判据。对于与STBC相关的基域，利用这些标准，通过Springer定理，构造几个显式的（双）四元数除法代数的无限族。这些用于获得新的$2\x 2$和$4\x 4$ STBC。
英文摘要：
In the context of space-time block codes (STBCs), the theory of generalized quaternion and biquaternion algebras (i.e., tensor products of two quaternion algebras) over arbitrary base fields is presented, as well as quadratic form theoretic criteria to check if such algebras are division algebras. For base fields relevant to STBCs, these criteria are exploited, via Springer's theorem, to construct several explicit infinite families of (bi-)quaternion division algebras. These are used to obtain new $2\x 2$ and $4\x 4$ STBCs.
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