Bounds on the minimum distance of additive quantum codes

Bounds on [[190,170]]₂

lower bound:	4
upper bound:	6
Construction

Construction of a [[190,170,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[190, 176, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 5, 7, 15, 18, 27, 32, 34, 43, 55, 56, 60, 65, 73, 78, 82, 84, 100, 105, 120, 121, 122, 123, 124, 126, 129, 148, 150, 154, 158, 161, 167, 170, 173, 182, 190, 191, 195, 203, 204, 206, 208, 209, 220, 221, 222, 224, 226, 228, 229, 230, 231, 232, 235, 238, 242, 243, 245, 246, 247, 249, 250, 251 }
[3]:  [[190, 170, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

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 [[190,170]]2

Construction

Notes

Bounds on [[190,170]]₂
