Bounds on the minimum distance of additive quantum codes
Bounds on [[125,92]]2
lower bound: | 6 |
upper bound: | 10 |
Construction
Construction of a [[125,92,6]] quantum code:
[1]: [[256, 222, 7]] quantum code over GF(2^2)
Extended BCH code with parameters 255 6
[2]: [[126, 92, 7]] quantum code over GF(2^2)
Shortening of [1] at { 7, 8, 13, 16, 18, 20, 22, 27, 28, 30, 34, 36, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 59, 69, 71, 74, 79, 80, 81, 82, 87, 89, 90, 95, 96, 97, 98, 99, 102, 103, 106, 112, 113, 115, 118, 119, 120, 122, 123, 125, 130, 131, 132, 134, 135, 137, 138, 140, 141, 147, 149, 150, 151, 153, 154, 155, 156, 157, 158, 160, 163, 164, 165, 167, 168, 169, 170, 171, 173, 176, 177, 178, 179, 180, 182, 183, 185, 186, 189, 191, 193, 194, 195, 196, 197, 198, 199, 200, 203, 204, 207, 209, 210, 212, 213, 217, 218, 223, 224, 227, 229, 232, 234, 235, 238, 239, 240, 245, 246, 247, 249, 251, 253, 255, 256 }
[3]: [[125, 92, 6]] quantum code over GF(2^2)
Puncturing of [2] at { 126 }
stabilizer matrix:
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[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 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 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 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 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1]
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