Bounds on the minimum distance of additive quantum codes

Bounds on [[157,137]]₂

lower bound:	4
upper bound:	6
Construction

Construction of a [[157,137,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[157, 143, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 6, 10, 13, 15, 19, 20, 26, 27, 34, 35, 36, 38, 40, 44, 52, 53, 56, 57, 61, 66, 67, 68, 70, 75, 76, 77, 81, 85, 86, 94, 95, 98, 99, 101, 105, 107, 108, 113, 115, 119, 122, 123, 124, 125, 126, 127, 131, 132, 134, 136, 141, 145, 150, 151, 157, 158, 164, 168, 169, 173, 174, 178, 195, 197, 198, 201, 202, 203, 204, 206, 209, 213, 217, 220, 223, 226, 227, 228, 229, 230, 235, 236, 238, 239, 241, 243, 244, 245, 246, 247, 248, 249, 250, 252 }
[3]:  [[157, 137, 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 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1|0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0]
      [0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0|1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1]
      [0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 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 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 0|0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1|0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 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 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0|0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 1|0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1|0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0]
      [0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0]
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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 1 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 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 1 0 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 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 [[157,137]]2

Construction

Notes

Bounds on [[157,137]]₂
