Bounds on the minimum distance of additive quantum codes

Bounds on [[72,39]]2

lower bound:7
upper bound:11

Construction

Construction of a [[72,39,7]] quantum code:
[1]:  [[128, 96, 7]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[72, 40, 7]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 7, 9, 11, 15, 17, 19, 23, 24, 32, 34, 38, 39, 40, 42, 44, 47, 48, 50, 53, 57, 58, 60, 61, 65, 68, 70, 71, 74, 78, 79, 80, 81, 82, 89, 90, 92, 95, 96, 97, 100, 102, 104, 109, 110, 111, 112, 113, 117, 118, 119, 122, 123, 125, 128 }
[3]:  [[72, 39, 7]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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