Abstract:
In this work a study of various methods of finite fields' construction in the Galois field $\mathrm{GF}(2^8)$ is carried out, and a comparative analysis of the speed of operation of the corresponding algorithms is presented. Implementation of these methods allow to realize further the effective Gao decoding algorithm, allowing to find and correct the errors that occur during the transmission of messages.
Keywords:Reed-Solomon codes, Galois field $\mathrm{GF}(2^8)$.
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