Bounds on the minimum distance of additive quantum codes
Bounds on [[147,120]]2
| lower bound: | 6 |
| upper bound: | 8 |
Construction
Construction of a [[147,120,6]] quantum code:
[1]: [[256, 230, 6]] quantum code over GF(2^2)
Extended BCH code with parameters 255 5
[2]: [[146, 120, 6]] quantum code over GF(2^2)
Shortening of [1] at { 2, 4, 5, 16, 18, 20, 21, 26, 27, 32, 33, 40, 43, 46, 47, 49, 52, 54, 55, 56, 59, 65, 66, 67, 70, 71, 72, 73, 77, 85, 87, 89, 92, 95, 98, 99, 100, 101, 102, 103, 105, 106, 107, 109, 110, 111, 116, 117, 120, 122, 125, 126, 128, 129, 130, 131, 132, 133, 135, 136, 140, 141, 144, 145, 147, 149, 153, 154, 155, 156, 162, 163, 164, 165, 166, 169, 170, 173, 175, 176, 177, 178, 183, 184, 185, 186, 190, 191, 198, 199, 200, 202, 207, 209, 210, 213, 214, 215, 217, 219, 221, 222, 223, 230, 232, 234, 239, 246, 248, 255 }
[3]: [[147, 120, 6]] quantum code over GF(2^2)
ExtendCode [2] by 1
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 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.
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Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024