Bounds on the minimum distance of additive quantum codes

Bounds on [[124,110]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[124,110,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[124, 110, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 5, 8, 10, 12, 13, 16, 19, 22, 28, 30, 35, 36, 37, 38, 39, 40, 48, 49, 51, 53, 57, 58, 61, 62, 65, 67, 68, 70, 71, 72, 75, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 91, 92, 95, 97, 98, 99, 100, 101, 103, 105, 106, 107, 108, 109, 110, 112, 114, 115, 117, 119, 120, 124, 125, 126, 128, 129, 130, 132, 135, 136, 137, 142, 147, 148, 155, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 173, 174, 176, 180, 182, 184, 185, 187, 188, 192, 193, 195, 196, 197, 199, 201, 207, 208, 209, 210, 212, 217, 218, 221, 222, 223, 224, 227, 237, 239, 241, 242, 243, 244, 245, 246, 247, 249, 250, 251 }

    stabilizer matrix:

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

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 [[124,110]]2

Construction

Notes

Bounds on [[124,110]]₂
