A Note on the Minimum Distance of Quantum LDPC Codes

  • Nicolas Delfosse
  • Zhentao Li
  • Stéphan Thomassé
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8635)


We provide a new lower bound on the minimum distance of a family of quantum LDPC codes based on Cayley graphs proposed by MacKay, Mitchison and Shokrollahi [14]. Our bound is exponential, improving on the quadratic bound of Couvreur, Delfosse and Zémor [3]. This result is obtained by examining a family of subsets of the hypercube which locally satisfy some parity conditions.


Minimum Distance Cayley Graph LDPC Code Minimum Cardinality Quantum Code 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Nicolas Delfosse
    • 1
  • Zhentao Li
    • 2
  • Stéphan Thomassé
    • 3
  1. 1.Département de PhysiqueUniversité de SherbrookeSherbrookeCanada
  2. 2.Département d’Informatique UMR CNRS 8548École Normale SupérieureFrance
  3. 3.LIP, UMR 5668, École Normale Supérieure de Lyon - CNRS - UCBL - INRIAUniversité de LyonFrance

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