Bounds on the minimum distance of additive quantum codes

Bounds on [[97,67]]2

lower bound:6
upper bound:9

Construction

Construction of a [[97,67,6]] quantum code:
[1]:  [[94, 67, 6]] quantum code over GF(2^2)
     quantum twisted code of length 94 with interval [ 1, 2, 3, 4 ] and parameter kappa 5
[2]:  [[97, 67, 6]] quantum code over GF(2^2)
     ExtendCode [1] by 3

    stabilizer matrix:

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

Notes


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