Bounds on the minimum distance of additive quantum codes

Bounds on [[62,4]]2

lower bound:14
upper bound:20

Construction

Construction of a [[62,4,14]] quantum code:
[1]:  [[62, 0, 18]] self-dual Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[58, 4, 14]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 59, 60, 61, 62 }
[3]:  [[62, 4, 14]] Quantum code over GF(2^2)
     ExtendCode [2] by 4

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0|0 0 0 1 1 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0|1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0|0 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0|0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0|1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0|1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0|1 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0|1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0|0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0|0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0|0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0|0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0|1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0|1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0|0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0|1 0 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0|0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0|0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0|1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0|0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0|0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0|0 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0|0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0|1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0|1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0|0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0|0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0]
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      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0|0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0]
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      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0|1 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0|1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0|1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0]
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last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014