Bounds on the minimum distance of additive quantum codes

Bounds on [[67,12]]2

lower bound:14
upper bound:20

Construction

Construction of a [[67,12,14]] quantum code:
[1]:  [[66, 12, 14]] quantum code over GF(2^2)
     ConstructionX using cyclic codes [65,39], [65,38], and auxiliary code [1,1]
[2]:  [[67, 12, 14]] quantum code over GF(2^2)
     ExtendCode [1] by 1

    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 1 0 0 0 1 1 1 1 1 0 0 0 0 0|1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 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 0 0 0 0 0 0 0 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 1 1 0 0 0 0|0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 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 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 1 1 0 0 0|0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 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 1 1 0 0|1 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 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 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 1 1 0 0|1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 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 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 0 0 1 1 0 0|1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 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 1 0 0 1 1 0 0 1 0 0|1 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0|0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 0|1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 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 1 1 1 1 1 0 1 1 0 1 0 0|0 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0|0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 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 1 0 0 1 0 0 0 0 1 1 1 0 0|0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 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 1 0 1 0 1 0 1 1 1 0 1 1 0 0|0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 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 1 1 0 1 1 0 1 0 0 1 0 1 0 0|1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 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 1 1 1 0 0 0 1 0 1 0 1 0 0 0|1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 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 1 1 1 0 0 0 1 0 1 0 1 0 0|1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 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 1 0 1 1 0 1 1 1 0 0 1 0 0 0|0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 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 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 1 1 0 1 1 1 0 0 1 0 0|0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 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 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 1 0 1 0 0 0 1 0 0 1 0 0 0 0|1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 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 0 0 0 1 0 0 1 0 0 0|1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 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 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 1 0 1 0 0 0 1 0 0 1 0 0|0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 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 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 0 0 1 1 0 1 1 1 1 0 0 0 0|0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 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 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 0 0 1 1 0 1 1 1 1 0 0 0|0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 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 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 0 0 1 1 0 1 1 1 1 0 0|1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 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 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 1 1 0 1 1 1 1 0 1 1 1 0 0|1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 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 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 1 1 1 1 1 0 0 0 0 0 1 1 0 0|0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 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 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 1 1 0 1 1 0 0 1 0 0 0 0|1 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0|1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0]
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last modified: 2013-12-13

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014