Bounds on the minimum distance of additive quantum codes
Bounds on [[108,73]]2
lower bound: | 7 |
upper bound: | 11 |
Construction
Construction of a [[108,73,7]] quantum code:
[1]: [[256, 222, 7]] quantum code over GF(2^2)
Extended BCH code with parameters 255 6
[2]: [[108, 74, 7]] quantum code over GF(2^2)
Shortening of [1] at { 1, 8, 10, 13, 16, 18, 19, 20, 21, 24, 25, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 43, 44, 45, 46, 50, 52, 53, 54, 55, 57, 58, 61, 63, 65, 69, 71, 72, 75, 76, 78, 79, 80, 81, 82, 84, 85, 87, 89, 93, 95, 96, 97, 100, 102, 103, 104, 105, 107, 111, 114, 115, 116, 117, 118, 122, 126, 128, 129, 134, 138, 141, 142, 143, 144, 146, 147, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 161, 163, 164, 166, 167, 168, 170, 172, 173, 175, 176, 179, 180, 181, 183, 184, 185, 187, 189, 190, 191, 192, 194, 196, 198, 199, 200, 202, 203, 208, 209, 210, 212, 214, 217, 219, 220, 221, 222, 223, 225, 229, 230, 232, 235, 239, 240, 243, 244, 245, 246, 247, 248, 249, 251, 252, 254, 255, 256 }
[3]: [[108, 73, 7]] quantum code over GF(2^2)
Subcode of [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 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 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.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014