### Quadratic Forms and Space-Time Block Codes from Generalized Quaternion and Biquaternion AlgebrasQuadratic Forms and Space-Time Block Codes from Generalized Quaternion and Biquaternion Algebras

Access Restriction
Open

 Author Unger, Thomas ♦ Markin, Nadya Source arXiv.org Content type Text File Format PDF Date of Submission 2008-07-01 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics Subject Keyword Computer Science - Information Theory ♦ cs ♦ math Abstract 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. Description Reference: IEEE Trans. Inform. Theory 57 (2011), no. 9, 6148-6156 Educational Use Research Learning Resource Type Article Page Count 8