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29 March 2024
 
  » arxiv » 1505.2111

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Power Decoding Reed--Solomon Codes Up to the Johnson Radius
Johan S. R. Nielsen ;
Date 8 May 2015
AbstractPower decoding, or "decoding using virtual interleaving" is a technique for decoding Reed--Solomon codes up to the Sudan radius. Since the method’s inception, it has been an open question if it possible to incorporate "multiplicities", the parameter allowing the Guruswami--Sudan algorithm to decode up to the Johnson radius. In this paper we show how this can be done, and describe how to efficiently solve the resulting key equations. We investigate its failure behaviour theoretically as well as giving simulation results, and we show how the method can be made practically faster using the re-encoding technique or a syndrome formulation.
Source arXiv, 1505.2111
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