Bounds on the minimum distance of additive quantum codes

Bounds on [[104,86]]2

lower bound:5
upper bound:6

Construction

Construction of a [[104,86,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[104, 86, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 4, 24, 69, 72, 79, 85, 86, 92, 93, 94, 99, 108, 109, 110, 112, 113, 115, 117 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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