On implementation of Reed–Solomon codes and decoding algorithms

In the paper a programming implementation of Reed–Solomon codes over a field $GF(2^8)$ is investigated. The implementation of encoding codes using discrete Fourier transform, decoding algorithm based on the Sugiyama method and the Gao decoding algorithm is given.
The paper is educational and methodical in nature and can help with the programming implementation of encoders and decoders of Reed – Solomon codes.