Bounds on the minimum distance of additive quantum codes
Bounds on [[116,68]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[116,68,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[116, 68, 9]] quantum code over GF(2^2)
Shortening of [1] at { 2, 3, 4, 5, 6, 8, 10, 13, 14, 15, 17, 18, 19, 20, 24, 25, 27, 30, 31, 32, 33, 34, 35, 36, 37, 39, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 57, 58, 59, 62, 63, 66, 69, 71, 72, 73, 75, 77, 83, 84, 86, 87, 88, 90, 92, 97, 98, 99, 102, 103, 104, 106, 107, 108, 109, 113, 114, 116, 117, 118, 120, 122, 123, 124, 126, 129, 130, 131, 132, 135, 136, 140, 141, 142, 144, 145, 147, 149, 150, 152, 153, 157, 158, 160, 163, 164, 169, 171, 175, 176, 178, 180, 184, 185, 188, 190, 192, 193, 194, 198, 200, 202, 204, 205, 206, 207, 211, 213, 215, 217, 220, 221, 222, 223, 225, 227, 229, 235, 236, 238, 239, 240, 243, 246, 247, 248, 249, 252, 254 }
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 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 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 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 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