Data transmition security with Reed-Solomon codes

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