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The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a scenario where the sender transmits a codeword from some codebook, and the receiver obtains N noisy outputs of the codeword. We study the problem of efficient reconstruction using N outputs that are each corrupted by at most t substitutions. Specifically, for the ubiquitous Reed-Solomon codes, we adapt the Koetter-Vardy soft-decoding algorithm, presenting a reconstruction algorithm capable of correcting beyond Johnson radius. Furthermore, the algorithm uses O (nN) field operations, where n is the codeword length.
Singhvi et al. (Tue,) studied this question.