Construction and decoding of matrix-product codes from nested codes

  • Fernando Hernando
  • Kristine Lally
  • Diego Ruano


We consider matrix-product codes \({[C_1\cdots C_s] \cdot A}\) , where \({C_1, \ldots , C_s}\) are nested linear codes and matrix A has full rank. We compute their minimum distance and provide a decoding algorithm when A is a non-singular by columns matrix. The decoding algorithm decodes up to half of the minimum distance.


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

Mathematics Subject Classification (2000)

94B05 94B35 94B65 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Fernando Hernando
    • 1
  • Kristine Lally
    • 2
  • Diego Ruano
    • 3
  1. 1.Department of MathematicsUniversity College CorkCorkIreland
  2. 2.Department of Mathematics and StatisticsRMIT UniversityMelbourneAustralia
  3. 3.Department of MathematicsTechnical University of DenmarkKgs. LyngbyDenmark

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