Bounds on the minimum distance of additive quantum codes
Bounds on [[109,60]]2
lower bound: | 9 |
upper bound: | 16 |
Construction
Construction of a [[109,60,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[108, 60, 9]] quantum code over GF(2^2)
Shortening of [1] at { 2, 4, 5, 7, 8, 10, 11, 12, 15, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33, 35, 36, 37, 40, 42, 43, 45, 47, 50, 51, 54, 56, 58, 61, 62, 64, 66, 68, 69, 70, 71, 74, 75, 76, 77, 79, 84, 88, 90, 91, 93, 94, 95, 98, 100, 102, 105, 109, 111, 112, 113, 114, 116, 121, 124, 125, 126, 129, 130, 131, 133, 134, 135, 136, 138, 139, 141, 142, 143, 146, 148, 149, 152, 153, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 168, 170, 171, 172, 174, 177, 179, 180, 181, 182, 184, 186, 189, 190, 191, 192, 193, 194, 196, 198, 201, 202, 204, 205, 206, 207, 208, 209, 210, 213, 215, 217, 218, 219, 221, 222, 223, 224, 225, 226, 228, 229, 230, 233, 236, 238, 240, 241, 243, 245, 249, 250, 252, 254 }
[3]: [[109, 60, 9]] quantum code over GF(2^2)
ExtendCode [2] by 1
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 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 1 0 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