Bounds on the minimum distance of additive quantum codes

Bounds on [[248,233]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[248,233,4]] quantum code:
[1]:  [[286, 272, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[248, 234, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 15, 17, 41, 43, 50, 103, 126, 127, 130, 160, 184, 185, 188, 190, 191, 203, 204, 236, 238, 240, 242, 251, 253, 255, 258, 262, 263, 265, 266, 268, 270, 272, 273, 280, 282, 283, 284, 286 }
[3]:  [[248, 233, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

last modified: 2009-02-08
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 necessarily 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: 10.06.2024
Bounds on the minimum distance of additive quantum codes

Bounds on [[248,233]]2

Construction

Notes

Bounds on [[248,233]]₂
