Bounds on the minimum distance of additive quantum codes

Bounds on [[125,111]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[125,111,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[125, 111, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 4, 6, 7, 9, 11, 12, 13, 14, 17, 22, 23, 25, 26, 27, 29, 31, 33, 34, 39, 40, 41, 43, 44, 45, 46, 47, 50, 52, 54, 58, 60, 62, 63, 64, 65, 66, 67, 68, 69, 74, 75, 77, 78, 81, 82, 83, 84, 85, 86, 87, 89, 90, 92, 93, 96, 101, 103, 104, 108, 109, 110, 111, 113, 115, 120, 122, 123, 127, 130, 131, 133, 134, 135, 138, 142, 143, 145, 149, 151, 152, 154, 158, 162, 165, 166, 169, 171, 173, 176, 177, 180, 188, 190, 191, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 208, 209, 210, 213, 216, 217, 218, 219, 221, 225, 231, 232, 234, 235, 240, 241, 243, 246, 247, 248, 249, 250 }

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0|0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0]
      [0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0|0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1]
      [0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 1 0 1 0|0 1 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1|0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0]
      [0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1|0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1]
      [0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0|0 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1]
      [0 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 0 0 0 0 0 0 0 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 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|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1|0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0]
      [0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1|0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1|0 0 0 1 1 1 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 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 0|0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0|0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 1 1 1 1 1 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 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]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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: 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 [[125,111]]2

Construction

Notes

Bounds on [[125,111]]₂
