Bounds on the minimum distance of additive quantum codes
Bounds on [[106,58]]2
lower bound: | 9 |
upper bound: | 16 |
Construction
Construction of a [[106,58,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[106, 58, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 3, 4, 6, 8, 10, 11, 13, 14, 16, 18, 19, 22, 23, 26, 27, 29, 30, 31, 32, 33, 36, 44, 45, 47, 51, 52, 53, 54, 55, 56, 59, 62, 63, 64, 66, 67, 68, 70, 72, 73, 74, 75, 76, 77, 80, 82, 83, 84, 85, 86, 90, 95, 96, 97, 99, 102, 104, 105, 108, 110, 111, 113, 114, 115, 116, 119, 120, 122, 123, 125, 127, 128, 129, 130, 132, 133, 137, 138, 139, 140, 142, 143, 144, 145, 146, 148, 149, 151, 152, 153, 156, 158, 159, 160, 161, 162, 165, 167, 168, 169, 170, 171, 173, 175, 179, 180, 182, 183, 184, 185, 186, 188, 189, 193, 194, 195, 196, 197, 198, 199, 201, 202, 204, 205, 206, 207, 208, 209, 211, 213, 214, 218, 222, 225, 228, 231, 237, 238, 239, 240, 241, 244, 245, 246, 248, 251, 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 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 0 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