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# A weight-based characterization of the set of correctable error patterns under list-of-2 decoding

• List decoding of block codes is an alternative approach to the decoding problem with appealing qualities. The fairly recent development of efficient algorithms for list decoding of Reed-Solomon codes spur new fuel to the study of this decoding strategy. In this paper we give a weight-based characterization of the set of correctable error patterns under list-of-2 ecoding of $(\tau, 2$)-list-decodable linear codes with known weight distribution. We apply our characterization of the set of correctable error patterns to a few codes in a family of low-rate list-of-2 decodable Reed-Solomon codes. We study the increase in error-correction performance obtained in a symmetric AWGN channel by using list-of-2 decoding instead of traditional decoding for these codes. Some simulation results for list-of-2 decoding on QAM channels using the Guruswami-Sudan algorithm for decoding of Reed-Solomon codes are also presented.
Mathematics Subject Classification: Primary: 94B05, 94B35, 94B70; Secondary: 11T71.

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