Bounds on the minimum distance of additive quantum codes
Bounds on [[166,142]]2
| lower bound: | 5 |
| upper bound: | 6 |
Construction
Construction of a [[166,142,5]] quantum code:
[1]: [[255, 231, 5]] quantum code over GF(2^2)
BCH code with parameters 255 5
[2]: [[166, 142, 5]] quantum code over GF(2^2)
Shortening of [1] at { 5, 19, 20, 24, 25, 26, 27, 29, 30, 31, 36, 39, 42, 45, 48, 50, 52, 53, 61, 66, 70, 76, 77, 92, 95, 98, 104, 109, 112, 115, 118, 122, 123, 124, 127, 128, 129, 130, 138, 139, 140, 159, 161, 172, 177, 179, 180, 181, 182, 183, 185, 186, 187, 189, 191, 192, 194, 197, 199, 200, 203, 205, 206, 209, 210, 212, 213, 214, 216, 222, 223, 226, 227, 229, 230, 234, 235, 237, 238, 240, 242, 245, 246, 247, 249, 250, 252, 253, 254 }
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0]
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[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 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.
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Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024