Bounds on the minimum distance of additive quantum codes
Bounds on [[93,75]]2
lower bound: | 4 |
upper bound: | 6 |
Construction
Construction of a [[93,75,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[92, 78, 4]] quantum code over GF(2^2)
Shortening of [1] at { 1, 4, 5, 6, 7, 8, 9, 10, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 49, 52, 54, 55, 58, 59, 61, 62, 63, 64, 65, 66, 67, 70, 72, 74, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 97, 98, 100, 101, 102, 103, 104, 107, 108, 109, 110, 111, 114, 115, 116, 117, 120, 123, 126, 127, 128, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 142, 145, 147, 149, 150, 152, 159, 160, 162, 163, 164, 166, 167, 168, 169, 170, 171, 177, 181, 183, 184, 188, 189, 190, 191, 192, 196, 198, 199, 200, 203, 207, 208, 211, 212, 213, 214, 216, 217, 218, 219, 221, 222, 225, 226, 228, 229, 231, 233, 235, 237, 238, 239, 241, 242, 245, 247, 249, 250, 252 }
[3]: [[92, 75, 4]] quantum code over GF(2^2)
Subcode of [2]
[4]: [[93, 75, 4]] quantum code over GF(2^2)
ExtendCode [3] by 1
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0|0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0|0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0|0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 0]
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[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 0 0|0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0]
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last modified: 2006-04-03
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 even 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
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Last change: 23.10.2014