Bounds on the minimum distance of additive quantum codes

Bounds on [[63,12]]2

lower bound:13
upper bound:18

Construction

Construction type: BierbrauerEdel

Construction of a [[63,12,13]] quantum code:
[1]:  [[63, 12, 13]] Quantum code over GF(2^2)
     quantum twisted code of length 63 with interval [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ] and parameter kappa 3

    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 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 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 1 0 1 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 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 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 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 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1]
      [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 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 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 0 0 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1]
      [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 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 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 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1]
      [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 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 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 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 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 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 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 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 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 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1]
      [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 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 1 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 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1]
      [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 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 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 1 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 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 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 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 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 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 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 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 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 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 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0]
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      [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 1 0 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 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 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 1 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 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 0 0 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 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 0 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 1 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1]
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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 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 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 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0]
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last modified: 2018-04-05

Notes


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