Quadratic Forms and Space-Time Block Codes From Generalized Quaternion and Biquaternion Algebras
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. F...
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| Veröffentlicht in: | IEEE transactions on information theory 2011-09, Vol.57 (9), p.6148-6156 |
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| container_title | IEEE transactions on information theory |
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| creator | Unger, T. Markin, N. |
| description | 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 × 2 and 4 × 4 STBCs. |
| doi_str_mv | 10.1109/TIT.2011.2161909 |
| format | Article |
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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. 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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 × 2 and 4 × 4 STBCs.</description><subject>Algebra</subject><subject>Applied sciences</subject><subject>Block codes</subject><subject>Coding, codes</subject><subject>Cost accounting</subject><subject>Division algebras</subject><subject>Exact sciences and technology</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>Matrices</subject><subject>quadratic forms</subject><subject>Quaternions</subject><subject>Signal and communications theory</subject><subject>space-time block codes</subject><subject>Telecommunications and information theory</subject><subject>Tensile stress</subject><subject>Theorems</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpFkM9PwjAUxxujiYjeTbw0Jh6H7fpj7RGIIAmJMc5z7bo3MxwbtOOgf71FCJ7er-_3vbwPQreUjCgl-jFf5KOUUDpKqaSa6DM0oEJkiZaCn6MBIVQlmnN1ia5CWMWSC5oO0Mfrzpbe9rXDs86vA7Ztid821kGS12vAk6ZzX3jalRDwzHdrPIcWvG3qHyhx9Pbg27pr_2yTevvfGDefUHgbrtFFZZsAN8c4RO-zp3z6nCxf5ovpeJk4lpI-qaxWsqKcFIoCF1AIyhWpMqFYqcFpmboCFFMxl6koGAOhdGml3j-WMcmG6P6wd-O77Q5Cb1bdzrfxpFGaU51xRaOIHETOdyF4qMzG12vrvw0lZo_RRIxmj9EcMUbLw3GvDc42lbetq8PJl3IhItUs6u4OuhoATmNJiJRMsF8jKHol</recordid><startdate>20110901</startdate><enddate>20110901</enddate><creator>Unger, T.</creator><creator>Markin, N.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| subjects | Algebra Applied sciences Block codes Coding, codes Cost accounting Division algebras Exact sciences and technology Information theory Information, signal and communications theory Matrices quadratic forms Quaternions Signal and communications theory space-time block codes Telecommunications and information theory Tensile stress Theorems |
| title | Quadratic Forms and Space-Time Block Codes From Generalized Quaternion and Biquaternion Algebras |
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