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Multi-trial Guruswami–Sudan decoding for generalised Reed–Solomon codes

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Abstract

An iterated refinement procedure for the Guruswami–Sudan list decoding algorithm for Generalised Reed–Solomon codes based on Alekhnovich’s module minimisation is proposed. The method is parametrisable and allows variants of the usual list decoding approach. In particular, finding the list of closest codewords within an intermediate radius can be performed with improved average-case complexity while retaining the worst-case complexity. We provide a detailed description of the module minimisation, reanalysing the Mulders–Storjohann algorithm and drawing new connections to both Alekhnovich’s algorithm and Lee–O’Sullivan’s. Furthermore, we show how to incorporate the re-encoding technique of Kötter and Vardy into our iterative algorithm.

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Acknowledgments

The authors thank Daniel Augot for fruitful discussions. This work has been supported by German Research Council Deutsche Forschungsgemeinschaft (DFG) under Grant BO 867/22-1 and Ze 1016/1-1.

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Author notes

  1. Alexander Zeh

    Present address: Computer Science Department, Technion—Israel Institute of Technology, Haifa, Israel

Authors and Affiliations

  1. Institute of Communications Engineering, University of Ulm, Ulm, Germany

    Johan S. R. Nielsen & Alexander Zeh

  2. Research Center INRIA Saclay - Île-de-France, École Polytechnique, Palaiseau, Paris, France

    Alexander Zeh

Authors
  1. Johan S. R. Nielsen
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  2. Alexander Zeh
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Correspondence to Johan S. R. Nielsen.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.

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Nielsen, J.S.R., Zeh, A. Multi-trial Guruswami–Sudan decoding for generalised Reed–Solomon codes. Des. Codes Cryptogr. 73, 507–527 (2014). https://doi.org/10.1007/s10623-014-9951-7

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  • DOI: https://doi.org/10.1007/s10623-014-9951-7

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