Bounds on the minimum distance of additive quantum codes
Bounds on [[168,130]]2
| lower bound: | 7 |
| upper bound: | 10 |
Construction
Construction of a [[168,130,7]] quantum code:
[1]: [[256, 222, 7]] quantum code over GF(2^2)
Extended BCH code with parameters 255 6
[2]: [[168, 134, 7]] quantum code over GF(2^2)
Shortening of [1] at { 7, 23, 25, 26, 30, 38, 45, 59, 60, 65, 79, 87, 95, 101, 112, 124, 125, 134, 135, 136, 137, 139, 140, 141, 142, 143, 147, 148, 149, 152, 154, 155, 156, 158, 160, 162, 165, 166, 167, 170, 173, 174, 175, 176, 177, 181, 184, 185, 186, 187, 189, 191, 194, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 215, 218, 219, 220, 221, 222, 223, 225, 226, 227, 231, 232, 233, 235, 237, 240, 244, 245, 247, 249, 254, 255 }
[3]: [[168, 130, 7]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 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 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 1 0 1]
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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.
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Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024