Bounds on the minimum distance of additive quantum codes
Bounds on [[126,77]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[126,77,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[125, 77, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 3, 4, 10, 11, 13, 15, 16, 19, 20, 21, 22, 24, 25, 26, 27, 29, 33, 35, 36, 38, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 53, 54, 56, 59, 60, 63, 67, 69, 74, 77, 78, 79, 80, 81, 82, 84, 86, 89, 93, 96, 98, 100, 102, 103, 108, 109, 110, 111, 112, 113, 114, 118, 122, 124, 127, 130, 131, 134, 138, 139, 141, 142, 145, 147, 149, 150, 153, 156, 157, 158, 159, 162, 163, 164, 168, 175, 176, 178, 180, 182, 183, 184, 185, 186, 189, 190, 194, 196, 197, 198, 201, 205, 207, 209, 211, 212, 213, 215, 219, 220, 221, 222, 224, 227, 228, 232, 233, 235, 237, 238, 240, 241, 242, 243, 244, 249, 251, 253, 254 }
[3]: [[126, 77, 9]] quantum code over GF(2^2)
ExtendCode [2] by 1
stabilizer matrix:
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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