Bounds on the minimum distance of additive quantum codes
Bounds on [[113,40]]2
| lower bound: | 13 |
| upper bound: | 25 |
Construction
Construction of a [[113,40,13]] quantum code:
[1]: [[255, 183, 13]] quantum code over GF(2^2)
BCH code with parameters 255 13
[2]: [[112, 40, 13]] quantum code over GF(2^2)
Shortening of [1] at { 1, 5, 6, 8, 12, 14, 18, 19, 20, 21, 22, 23, 26, 30, 31, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 54, 55, 57, 60, 61, 64, 66, 67, 68, 69, 70, 71, 72, 75, 78, 80, 82, 83, 84, 85, 87, 89, 90, 92, 93, 96, 97, 101, 104, 106, 108, 109, 111, 114, 115, 116, 118, 119, 120, 122, 127, 128, 130, 132, 133, 136, 138, 139, 140, 142, 143, 144, 145, 149, 150, 152, 154, 158, 159, 160, 163, 164, 168, 169, 171, 173, 176, 177, 178, 180, 181, 182, 186, 187, 189, 194, 195, 196, 200, 202, 205, 208, 209, 210, 211, 213, 214, 216, 217, 218, 219, 221, 222, 223, 224, 225, 227, 228, 229, 230, 231, 232, 233, 234, 237, 240, 241, 244, 245, 246, 249, 250, 252 }
[3]: [[113, 40, 13]] quantum code over GF(2^2)
ExtendCode [2] by 1
stabilizer matrix:
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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
(codes@codetables.de).
Last change: 23.10.2014