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Spread spectrum modulator
Lejsková, Alena ; Kováč, Michal (referee) ; Maršálek, Roman (advisor)
This thesis deals with a method of spectrum-spreading of the data signals transmitted in the radio channel. There exist three different ways of spreading application, they uses pseudorandom sequences and also orthogonal sequences. In these systems we can find various kinds of modulations, one of them (Quadrature Phase Shift Keying) is shown at the end of the thesis. Spectrum spreading orthogonal multiplex OFDM is based on this method. The thesis wants to present the principle of the spectrum spreading method and the description of systems, transmitters and receivers that are using this method.
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Matrices with Entries -1, 1, 0
Píšová, Vendula ; Škorpilová, Martina (advisor) ; Bečvář, Jindřich (referee)
In this thesis we introduce selected classes of matrices, whose entries are only numbers −1, 1, 0. We combine existing results from various fields of Mathematics and enrich them with specific examples and explanations, with the aim of making the understanding of the text easier. Thanks to that, the reader can comprehend the theory and look under the hood of non-trivial applications. We will start with introducing adjacency matrices and covering of complete graphs with complete bipartite graphs. Then we follow with Hadamard matrices and will show the conditions for their constructions. Incidence matrices of the set systems will help us solve the combinatorial problem of the Odd-town clubs. Finally, we will prove the Cayley formula about the spanning trees of the complete graph, using incidence matrices.
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Hadamard matrices and their applications in cryptography
Luber, Jan ; Drápal, Aleš (advisor) ; Žemlička, Jan (referee)
Title: Hadamard matrices and their applications in cryptography Author: Jan Luber Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc., Department of Algebra Abstract: This thesis takes interest in Hadamard matrices, their constructions and application in cryptography. Firstly, we introduce basic properties of Hadamard matrices and selected summary of classical constructions is presented. Then we show a table of constructions that can be used to construct Hadamard matrix of given order. In the next part, we get concerned with Hadamard matrices with circulant cores with detailed description of construction Hadamard matrices with two circulant cores from GL-pair. In the end, we present cryptosystem using Hadamard matrices, we show its essential weaknesses and simple attacks. We propose several improvements in the form of adding other security elements. Keywords: Hadamard matrix, Hadamard conjecture, symmetric cryptography
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Spread spectrum modulator
Lejsková, Alena ; Kováč, Michal (referee) ; Maršálek, Roman (advisor)
This thesis deals with a method of spectrum-spreading of the data signals transmitted in the radio channel. There exist three different ways of spreading application, they uses pseudorandom sequences and also orthogonal sequences. In these systems we can find various kinds of modulations, one of them (Quadrature Phase Shift Keying) is shown at the end of the thesis. Spectrum spreading orthogonal multiplex OFDM is based on this method. The thesis wants to present the principle of the spectrum spreading method and the description of systems, transmitters and receivers that are using this method.
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