Bounds on the minimum distance of additive quantum codes

Bounds on [[96,74]]₂

lower bound:	5
upper bound:	6
Construction

Construction of a [[96,74,5]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[127, 106, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 128
[3]:  [[95, 74, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 3, 4, 11, 12, 13, 21, 28, 33, 37, 38, 42, 49, 51, 54, 59, 62, 63, 64, 68, 72, 76, 79, 85, 87, 88, 92, 96, 102, 110, 117, 119, 127 }
[4]:  [[96, 74, 5]] quantum code over GF(2^2)
     ExtendCode [3] by 1

    stabilizer matrix:

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

last modified: 2006-04-03
Notes

All codes establishing the lower bounds where constructed using MAGMA.
Most upper bounds on qubit codes for n≤100 are based on a MAGMA program by Eric Rains.
For n>100, the upper bounds on qubit codes are weak (and not even monotone in k).
Some additional information can be found in the book by Nebe, Rains, and Sloane.
My apologies to all authors that have contributed codes to this table for not giving specific credits.
This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014
Bounds on the minimum distance of additive quantum codes

Bounds on [[96,74]]2

Construction

Notes

Bounds on [[96,74]]₂
