Bounds on the minimum distance of additive quantum codes
Bounds on [[173,153]]2
| lower bound: | 4 |
| upper bound: | 6 |
Construction
Construction of a [[173,153,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[173, 159, 4]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 4, 8, 11, 12, 19, 24, 25, 28, 32, 34, 36, 38, 39, 54, 61, 63, 64, 72, 78, 80, 91, 93, 95, 96, 103, 105, 106, 115, 116, 119, 121, 122, 124, 125, 130, 133, 143, 145, 152, 165, 172, 175, 184, 185, 192, 193, 194, 195, 198, 199, 206, 209, 211, 214, 221, 224, 225, 226, 228, 229, 230, 231, 233, 234, 235, 236, 237, 241, 242, 243, 244, 246, 248, 249, 250, 251, 252 }
[3]: [[173, 153, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 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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Last change: 10.06.2024