Structure analysis for Reed-Solomon codes and fast decoding method

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In the following, we summarize the main results of our studies.1. A new decoding method for shortended Reed-Solomon codesWe proposed a decoding algorithm for shortended Reed-Solomon codes using some information which is shortended symbol positions.2. Decoding of Reed-Solomon codes beyond the error-correction boundWe proposed a decoding method of Reed-Solomon codes beyond the error-correction bound. Our method is based on the histgram decoding and remainder decoding.3. On computing the local distance profile for cyclic codesWe proposed a method for computing the local distance profile of cyclic codes. Using our method, we can obtain the upper bound for decoding error probability. It is tighter than the usual upper bound (union bound).