Bounds on the minimum distance of additive quantum codes

Bounds on [[76,48]]2

lower bound:6
upper bound:9

Construction

Construction of a [[76,48,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[72, 49, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 4, 5, 7, 8, 14, 15, 16, 18, 19, 21, 22, 23, 34, 35, 36, 37, 40, 43, 48, 49, 51, 53, 58, 59, 60, 63, 66, 67, 68, 70, 71, 74, 75, 81, 84, 85, 89, 90, 92, 94, 95, 99, 100, 103, 105, 107, 108, 111, 112, 114, 115, 120, 124, 125, 126 }
[3]:  [[72, 48, 6]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[76, 48, 6]] quantum code over GF(2^2)
     ExtendCode [3] by 4

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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