Designs, Codes and Cryptography

, Volume 73, Issue 2, pp 507–527 | Cite as

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

  • Johan S. R. Nielsen
  • Alexander Zeh


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.


Guruswami–Sudan List decoding Multi-trial Reed–Solomon codes Re-encoding transformation 

Mathematics Subject Classification

68P30 94B35 



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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of Communications EngineeringUniversity of UlmUlmGermany
  2. 2.Research Center INRIA Saclay - Île-de-France, École PolytechniquePalaiseau, ParisFrance
  3. 3.Computer Science DepartmentTechnion—Israel Institute of TechnologyHaifaIsrael

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