Quantum Codes

  • Gabriele Nebe
  • Eric M. Rains
  • Neil J.A. Sloane
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 17)


Quantum codes, and especially the additive and symplectic constructions thereof, were one of the reasons for our initial interest in the Clifford- Weil group. General quantum codes behave in many ways like classical selforthogonal codes, and there are strong connections with the theory of self-dual codes. In particular, Theorems 11.1.12, 11.1.16, 11.1.26 and 11.1.32 of Chapter 11 are all based on phenomena first noticed for quantum codes (more precisely, for codes of Type 4H+, but as we will see, the two are extremely closely related). There is also a direct connection: the natural group of equivalences acting on a symplectic quantum code is exactly the complex Clifford group X m = C m (.(2II)) (cf. Theorem 6.2.1).


Hermitian Operator Partial Trace Quantum Code Additive Code Weight Enumerator 
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Copyright information

© Springer 2006

Authors and Affiliations

  • Gabriele Nebe
    • 1
  • Eric M. Rains
    • 2
  • Neil J.A. Sloane
    • 3
  1. 1.Lehrstuhl D für Mathematik Rheinisch-Westfälische Technische Hochschule AachenAachenGermany
  2. 2.Department of MathematicsUniversity of California at DavisDavisUSA
  3. 3.Internet and Network Systems Research AT&T Shannon LabsFlorham ParkUSA

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