Bounds on the minimum distance of additive quantum codes
Bounds on [[112,64]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[112,64,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[112, 64, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 4, 5, 7, 8, 9, 10, 11, 12, 17, 19, 21, 23, 25, 26, 28, 31, 32, 33, 34, 35, 37, 38, 39, 42, 43, 45, 46, 48, 51, 52, 53, 55, 56, 64, 65, 66, 70, 73, 75, 76, 77, 78, 79, 82, 84, 86, 91, 93, 97, 98, 102, 104, 107, 109, 110, 112, 116, 117, 118, 119, 120, 122, 124, 125, 128, 131, 132, 134, 135, 136, 137, 139, 141, 142, 145, 146, 148, 149, 153, 154, 155, 157, 158, 159, 162, 163, 164, 165, 166, 167, 168, 169, 171, 173, 175, 176, 177, 178, 179, 180, 181, 184, 190, 191, 192, 193, 195, 196, 198, 200, 201, 202, 204, 205, 206, 210, 212, 214, 215, 218, 220, 221, 222, 226, 227, 229, 231, 233, 235, 236, 238, 239, 240, 242, 245, 246, 248, 249, 251, 252, 254, 255 }
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 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 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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Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014