Bounds on the minimum distance of additive quantum codes
Bounds on [[111,76]]2
lower bound: | 7 |
upper bound: | 10 |
Construction
Construction of a [[111,76,7]] quantum code:
[1]: [[256, 222, 7]] quantum code over GF(2^2)
Extended BCH code with parameters 255 6
[2]: [[110, 76, 7]] quantum code over GF(2^2)
Shortening of [1] at { 2, 4, 5, 6, 7, 8, 11, 12, 13, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 45, 46, 47, 49, 50, 54, 55, 56, 59, 60, 62, 63, 64, 65, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 88, 91, 92, 95, 97, 98, 99, 101, 102, 104, 105, 109, 110, 111, 112, 114, 115, 117, 118, 119, 120, 121, 124, 126, 128, 130, 131, 135, 138, 141, 142, 146, 147, 148, 151, 153, 158, 159, 160, 162, 165, 173, 176, 177, 178, 180, 181, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 199, 201, 202, 203, 205, 206, 209, 211, 212, 214, 216, 217, 218, 220, 224, 225, 226, 228, 229, 230, 231, 233, 237, 238, 242, 250, 254, 255 }
[3]: [[111, 76, 7]] quantum code over GF(2^2)
ExtendCode [2] by 1
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 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0]
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