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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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Data transmition security with Reed-Solomon codes
Šalanský, Jan ; Šporik, Jan (referee) ; Němec, Karel (advisor)
This Bachelor thesis deals with the security of data transmission by Reed-Solomon codes. It discusses the design of the code, coding method and primarily decoding facility. There are described particular phases of decoding: the computation of the Syndrome, determination of an error locator polynomial, finding of positions of false symbols by Chien search and calculation of error values using the Forney’s algorithm. It compares these basic algorithms to find the polynomial localization errors: Peterson-Gorenstein-Zierler algorithm, Berlekamp-Massey algorithm and the extended Euclidean algorithm. There is shown a detailed design and software implementation of a simple system with forward error correction based on these theoretical findings. Design of the system begins by selecting the appropriate Reed-Solomon code RS (63,39). Next step is construction of basic algebraic structures for this code and derivation of encoder and decoder. Design of system with forward error correction finishes by calculation of encoding and decoding. The final system with forward error correction has been programmed for platforms MS Windows and Linux. It has been based on previous calculations and examples in references.
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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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Data transmition security with Reed-Solomon codes
Šalanský, Jan ; Šporik, Jan (referee) ; Němec, Karel (advisor)
This Bachelor thesis deals with the security of data transmission by Reed-Solomon codes. It discusses the design of the code, coding method and primarily decoding facility. There are described particular phases of decoding: the computation of the Syndrome, determination of an error locator polynomial, finding of positions of false symbols by Chien search and calculation of error values using the Forney’s algorithm. It compares these basic algorithms to find the polynomial localization errors: Peterson-Gorenstein-Zierler algorithm, Berlekamp-Massey algorithm and the extended Euclidean algorithm. There is shown a detailed design and software implementation of a simple system with forward error correction based on these theoretical findings. Design of the system begins by selecting the appropriate Reed-Solomon code RS (63,39). Next step is construction of basic algebraic structures for this code and derivation of encoder and decoder. Design of system with forward error correction finishes by calculation of encoding and decoding. The final system with forward error correction has been programmed for platforms MS Windows and Linux. It has been based on previous calculations and examples in references.
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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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