Bounds on the minimum distance of additive quantum codes
Bounds on [[109,59]]2
lower bound: | 9 |
upper bound: | 16 |
Construction
Construction of a [[109,59,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[107, 59, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 4, 5, 7, 8, 9, 12, 14, 15, 16, 17, 18, 19, 21, 22, 25, 26, 28, 29, 33, 34, 35, 37, 38, 39, 40, 42, 45, 48, 49, 50, 51, 54, 55, 56, 59, 62, 63, 65, 66, 69, 71, 73, 74, 79, 82, 83, 85, 86, 88, 89, 91, 93, 97, 98, 100, 101, 102, 103, 104, 105, 106, 109, 110, 111, 112, 114, 117, 118, 119, 122, 123, 124, 127, 129, 130, 131, 132, 135, 136, 137, 143, 144, 148, 149, 150, 151, 152, 155, 156, 158, 159, 161, 162, 164, 166, 167, 168, 169, 174, 182, 183, 184, 186, 187, 190, 191, 193, 195, 196, 197, 198, 200, 201, 202, 203, 205, 206, 209, 210, 211, 212, 214, 215, 216, 217, 218, 219, 221, 223, 226, 229, 230, 231, 232, 233, 234, 236, 237, 238, 242, 243, 248, 249, 252, 253, 254 }
[3]: [[109, 59, 9]] quantum code over GF(2^2)
ExtendCode [2] by 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 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0]
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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