Bounds on the minimum distance of additive quantum codes

Bounds on [[175,156]]₂

lower bound:	4
upper bound:	5
Construction

Construction of a [[175,156,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[175, 161, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 7, 10, 17, 24, 26, 28, 32, 33, 41, 42, 44, 47, 57, 58, 60, 64, 67, 73, 80, 82, 83, 87, 91, 95, 99, 107, 115, 116, 118, 119, 123, 125, 131, 143, 145, 149, 152, 154, 161, 163, 166, 169, 174, 180, 184, 185, 186, 192, 195, 200, 207, 208, 214, 217, 218, 220, 221, 222, 223, 224, 226, 227, 228, 232, 234, 236, 238, 239, 240, 241, 245, 247, 248, 249, 250, 251, 252 }
[3]:  [[175, 156, 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 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 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 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 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 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 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 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1|1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 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 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 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 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 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 0 0 1 0 0 0 0 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 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 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 1 1 0 1 1 1 1 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 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 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 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 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 1 1 0 1 1 1 1 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 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0|0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 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 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 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 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1]
      [0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1|0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1|0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1]
      [0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0|0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 0|0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1]
      [0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0|0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0|0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0]
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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 [[175,156]]2

Construction

Notes

Bounds on [[175,156]]₂
