Designs, Codes and Cryptography

, Volume 73, Issue 2, pp 417–424 | Cite as

Quantum codes from nearly self-orthogonal quaternary linear codes

  • Petr LisoněkEmail author
  • Vijaykumar Singh


Construction X and its variants are known from the theory of classical error control codes. We present instances of these constructions that produce binary stabilizer quantum error control codes from arbitrary quaternary linear codes. Our construction does not require the classical linear code \(C\) that is used as the ingredient to satisfy the dual containment condition, or, equivalently, \(C^{\perp _h}\) is not required to satisfy the self-orthogonality condition. We prove lower bounds on the minimum distance of quantum codes obtained from our construction. We give examples of record breaking quantum codes produced from our construction. In these examples, the ingredient code \(C\) is nearly dual containing, or, equivalently, \(C^{\perp _h}\) is nearly self-orthogonal, by which we mean that \(\dim (C^{\perp _h})-\dim (C^{\perp _h}\cap C)\) is positive but small.


Quantum error-correcting code Linear code Construction X 

Mathematics Subject Classification

94B05 94B15 



This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Collaborative Research Group “Mathematics of Quantum Information” of the Pacific Institute for the Mathematical Sciences (PIMS).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada

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