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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.
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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.
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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.
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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.
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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.
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