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National Repository of Grey Literature 3 records found  Search took 0.01 seconds. 
Structure of division rings
 Reichel, Tomáš ; Žemlička, Jan (advisor) ; Šaroch, Jan (referee)
This bachelor thesis deals with a theorem and its proof, which allows construction of division ring from cyclic field extension which satisfies certain conditions. The reader is expected to have basic knowledge of linear algebra, ring and module theory. For using this theorem the reader also needs some skills in counting Galois groups. In this work there are also included two basic examples of usage the theorem. During the proof we introduce a structure of tensor product and Brauer group. Powered by TCPDF (www.tcpdf.org)
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Structure of division rings
 Reichel, Tomáš ; Žemlička, Jan (advisor) ; Šaroch, Jan (referee)
This bachelor thesis deals with a theorem and its proof, which allows construction of division ring from cyclic field extension which satisfies certain conditions. The reader is expected to have basic knowledge of linear algebra, ring and module theory. For using this theorem the reader also needs some skills in counting Galois groups. In this work there are also included two basic examples of usage the theorem. During the proof we introduce a structure of tensor product and Brauer group. Powered by TCPDF (www.tcpdf.org)
Detailed record
Division rings in coding theory
 Svatoňová, Petra ; Žemlička, Jan (advisor) ; Holub, Štěpán (referee)
Wireless communication using multiple transmit and receive antennas is very effective when suitable space-time codes are used. Reliability of codes for com- munication can be assessed using various criteria. One of the basic is the Rank Criterion. In the presented work, we focus on this criterion and using division algebras we construct space-time block codes that satisfy it. First, we introduce the general construction. Then we apply it to create specific examples of division algebras and respective codes. At the end, we follow up with the Coding Gain Criterion - we present the Golden Code and using division algebras we outline general construction of perfect space-time codes.
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