List decoding of repeated codes

  • Fernando Hernando
  • Michael O’Sullivan
  • Diego Ruano
Original Paper


Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to their parameters, we show that they have a good performance with this algorithm. We compare, by computer simulations, our algorithm for the repeated code of a Reed–Solomon code against a decoding algorithm of a Reed–Solomon code. Finally, we estimate the decoding capability of the algorithm for Reed–Solomon codes and show that performance is somewhat better than our estimates.


Linear codes Matrix-product codes Decoding algorithm  Minimum distance Quasi-cyclic codes 

Mathematics Subject Classification (2000)

94B05 94B35 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Fernando Hernando
    • 1
    • 2
  • Michael O’Sullivan
    • 3
  • Diego Ruano
    • 4
  1. 1.Department of MathematicsUniversidad Jaume ICampus Riu Sec Castellón de la PlanaSpain
  2. 2.Department of Mathematical SciencesAalborg UniversityAalborgDenmark
  3. 3.Department of Mathematics and StatisticsSan Diego State UniversitySan DiegoUSA
  4. 4.Department of Mathematical SciencesAalborg UniversityAalborg ØstDenmark

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