Bounds on the minimum distance of additive quantum codes
Bounds on [[106,71]]2
lower bound: | 7 |
upper bound: | 11 |
Construction
Construction of a [[106,71,7]] quantum code:
[1]: [[256, 222, 7]] quantum code over GF(2^2)
Extended BCH code with parameters 255 6
[2]: [[106, 72, 7]] quantum code over GF(2^2)
Shortening of [1] at { 2, 3, 5, 6, 7, 8, 11, 13, 16, 18, 19, 22, 23, 26, 27, 28, 29, 30, 32, 33, 35, 36, 37, 39, 41, 43, 44, 45, 47, 48, 49, 50, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 67, 68, 71, 77, 79, 80, 81, 84, 85, 87, 88, 91, 93, 95, 97, 101, 102, 103, 104, 108, 109, 110, 112, 113, 118, 119, 120, 122, 124, 125, 126, 127, 129, 130, 131, 133, 135, 141, 142, 143, 144, 146, 147, 148, 150, 152, 153, 154, 156, 157, 158, 159, 160, 162, 166, 168, 170, 172, 173, 174, 179, 180, 181, 184, 185, 187, 190, 192, 194, 195, 196, 198, 200, 201, 204, 206, 213, 214, 216, 217, 218, 219, 222, 224, 225, 226, 227, 229, 230, 231, 232, 233, 234, 236, 237, 239, 240, 241, 245, 246, 248, 250, 252, 253, 254, 255, 256 }
[3]: [[106, 71, 7]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0|0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 0 1]
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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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