Bounds on the minimum distance of additive quantum codes

Bounds on [[117,108]]2

lower bound:3
upper bound:3

Construction

Construction of a [[117,108,3]] quantum code:
[1]:  [[168, 159, 3]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[117, 108, 3]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 10, 13, 16, 20, 21, 22, 25, 26, 28, 29, 30, 32, 35, 39, 44, 50, 53, 54, 57, 58, 59, 60, 61, 65, 68, 69, 71, 76, 78, 80, 81, 125, 127, 129, 133, 134, 135, 136, 138, 139, 142, 148, 154, 157, 158, 159, 161, 162, 165, 166 }

    stabilizer matrix:

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

last modified: 2008-08-05

Notes


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