Bounds on the minimum distance of additive quantum codes

Bounds on [[208,191]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[208,191,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[208, 194, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 18, 26, 36, 48, 63, 65, 67, 84, 88, 95, 105, 115, 116, 117, 120, 121, 124, 126, 144, 164, 165, 190, 194, 200, 208, 209, 221, 223, 224, 226, 227, 228, 230, 232, 234, 235, 237, 239, 240, 242, 243, 247, 249, 251 }
[3]:  [[208, 191, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 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 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 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 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 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 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1|1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 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 1 0 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 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 1 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 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 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 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 0 1 1 1 1 0 0 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 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1|0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 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 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 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 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1]
      [0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 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 1 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0|0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1]
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      [0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 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 0 0 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0|0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 1]
      [0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 1|0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1]
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      [0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1|0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 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 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1]
      [0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 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 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1|0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0]
      [0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0|0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 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 [[208,191]]2

Construction

Notes

Bounds on [[208,191]]₂
