Bounds on the minimum distance of additive quantum codes

Bounds on [[92,66]]2

lower bound:6
upper bound:8

Construction

Construction of a [[92,66,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[90, 67, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 37, 58, 62, 65, 70, 73, 74, 78, 79, 80, 81, 82, 83, 84, 85, 88, 91, 92, 93, 94, 96, 97, 100, 101, 103, 104, 107, 109, 111, 114, 115, 116, 118, 119, 123, 126, 127, 128 }
[3]:  [[90, 66, 6]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[92, 66, 6]] quantum code over GF(2^2)
     ExtendCode [3] by 2

    stabilizer matrix:

      [1 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 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 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 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 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 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0|0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 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 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 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 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 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 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 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 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 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 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 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 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 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 1 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 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 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0|0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0|0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 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 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0]

last modified: 2006-04-03

Notes


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