Bounds on the minimum distance of additive quantum codes
Bounds on [[124,88]]2
lower bound: | 7 |
upper bound: | 11 |
Construction
Construction of a [[124,88,7]] quantum code:
[1]: [[256, 222, 7]] quantum code over GF(2^2)
Extended BCH code with parameters 255 6
[2]: [[122, 88, 7]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 51, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 68, 69, 70, 71, 74, 76, 77, 79, 81, 82, 84, 87, 88, 89, 90, 91, 92, 93, 95, 97, 98, 100, 101, 102, 103, 104, 107, 110, 111, 112, 114, 116, 117, 118, 119, 121, 122, 128, 130, 138, 144, 146, 148, 149, 154, 155, 157, 159, 161, 164, 168, 169, 176, 177, 183, 186, 187, 190, 192, 195, 197, 198, 206, 209, 210, 211, 213, 214, 217, 218, 219, 222, 226, 227, 228, 230, 234, 235, 236, 238, 243, 245, 250, 254, 255, 256 }
[3]: [[124, 88, 7]] quantum code over GF(2^2)
ExtendCode [2] by 2
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