|
|
BCH codes
Frolka, Jakub ; Šilhavý, Pavel (referee) ; Šedý, Jakub (advisor)
The work deals with data security using BCH codes. In the work are described BCH codes in binary and non-binary form, and their most important subclass RS codes. Furthermore, this work describes the method of decoding Peterson-Gorenstein-Zierl, Berlekamp- Massey and Euclidean algorithm. For the presentation of encoding and decoding process, the application was created in Matlab, which has two parts – Learning BCH codes and Simulation of BCH codes. Using the generated application performance of BCH codes was compared at the last part of the work.
|
|
|
Comparison of decoding algorithms of Reed-Solomon code
Šicner, Jiří ; Krajsa, Ondřej (referee) ; Šilhavý, Pavel (advisor)
The work deals with the encoding and decoding of Reed-Solomon codes. There is generally described algebraic decoding of Reed-Solomon codes, and then described four methods of decoding, namely Massey-Berlekamp algorithm, Euclidean algoritus, Peterson-Gorenstein-Zierler algorithm and the direct method. These methods are then compared, and some of them are implemented in Matlab.
|
|
|
Analysis of Computational Effort of Self-Correcting Codes
Bártů, Tomáš ; Drábek, Vladimír (referee) ; Bidlo, Michal (advisor)
The work deals with error-correcting codes, specifically encoding and decoding Reed-Solomon codes. An introduction to error-correcting codes is provided, followed by a description of the encoding and decoding principle of Reed-Solomon codes using the Petterson-Gorenstein-Zierler, Berlekamp-Massey, and Euclidean algorithms. Implementation is then described, which realizes some of the mentioned algorithms. This is followed by experiments with applications that compare the time and iteration complexity of the encoding and decoding processes.
|
|
| |
|
|
Modular algorithms and interpolation
Kubát, David ; Stanovský, David (advisor) ; Žemlička, Jan (referee)
This thesis concerns with the polynomial interpolation problem and the rational function reconstruction problem (Cauchy interpolation, Padé approximation). It does so from the algebraical point of view. Moreover, it involves some applications of the generalized Chinese remainder theorem (Hermite interpolation, partial fraction decomposition). An important theoretical concept regarding the above mentioned problems is the Euclidean algorithm, which is studied in case of polynomial rings. The structure of the thesis is based on the book by von zur Gathen and Gerhard called Modern Computer Algebra. Its exercises are the main content of the thesis. They usually extend the theory involved. Powered by TCPDF (www.tcpdf.org)
|
|
|
Theory of Numbers in Ancient Greece
Smrčka, Zdeněk ; Bečvář, Jindřich (advisor) ; Halas, Zdeněk (referee)
Title: Theory of Numbers in Ancient Greece Author: Bc. Zdenek Smrcka Department: The Department of Mathematics Education Supervisor: doc. RNDr. Jindřich Bečvář, CSc. Abstract: The goal of this thesis is to write up clearly and comprehensibly numeric theoretical research and its results in Ancient Greece between 6 century before Christ and 4 century after Christ. In this thesis we try show examples use of Greece's Mathematics for improvement teaching in education and better understanding abstract thinking in Mathematics. We want so that students understand thinking and abilities Greece's mathematicians. We compare high school view on searching greatest common divisor and Euclidean algorithm. We present important Greece's knowledges as sieve of Eratosthenes, arithmetic of Diofantos etc.. Something of Greece's knowledges as Euclidean algorithm, sieve of Eratosthenes etc. are use of up to now. Keywords: Mathematics in Ancient Greece, figurate number, theory of numbers, Continual fraction, Euclidean algorithm
|
|
|
BCH codes
Frolka, Jakub ; Šilhavý, Pavel (referee) ; Šedý, Jakub (advisor)
The work deals with data security using BCH codes. In the work are described BCH codes in binary and non-binary form, and their most important subclass RS codes. Furthermore, this work describes the method of decoding Peterson-Gorenstein-Zierl, Berlekamp- Massey and Euclidean algorithm. For the presentation of encoding and decoding process, the application was created in Matlab, which has two parts – Learning BCH codes and Simulation of BCH codes. Using the generated application performance of BCH codes was compared at the last part of the work.
|
|
|
Comparison of decoding algorithms of Reed-Solomon code
Šicner, Jiří ; Krajsa, Ondřej (referee) ; Šilhavý, Pavel (advisor)
The work deals with the encoding and decoding of Reed-Solomon codes. There is generally described algebraic decoding of Reed-Solomon codes, and then described four methods of decoding, namely Massey-Berlekamp algorithm, Euclidean algoritus, Peterson-Gorenstein-Zierler algorithm and the direct method. These methods are then compared, and some of them are implemented in Matlab.
|
guest ::
