A novel method to obtain a basis for all possible solutions for decoding Reed-Solomon (RS) codes is given, using an intermediate result of decoding obtained by the Extended Euclidean Algorithm. The unknowns of the possible solutions can be calculated if reliability information is available. Numerical results show that this approach has a superior performance compared to Generalized Minimum Distance decoding [1]. Further, the new method has for a relatively high-rate RS code a lower complexity and a lower error rate when compared to the Koetter-Vardy algorithm [2].
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