Bounds on the minimum distance of additive quantum codes
Bounds on [[158,143]]2
| lower bound: | 4 |
| upper bound: | 4 |
Construction
Construction of a [[158,143,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[158, 144, 4]] quantum code over GF(2^2)
Shortening of [1] at { 7, 11, 18, 21, 22, 24, 28, 29, 31, 33, 35, 36, 38, 40, 42, 47, 58, 59, 60, 63, 67, 80, 81, 83, 85, 94, 99, 103, 105, 106, 107, 108, 109, 112, 114, 116, 119, 122, 123, 124, 125, 126, 138, 144, 145, 146, 150, 153, 154, 161, 162, 163, 167, 170, 172, 173, 174, 175, 177, 179, 181, 182, 184, 185, 186, 192, 193, 194, 208, 211, 213, 216, 220, 223, 224, 225, 227, 228, 229, 230, 232, 234, 237, 238, 239, 240, 242, 245, 246, 247, 249, 250, 251, 252 }
[3]: [[158, 143, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 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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Last change: 10.06.2024