Bounds on the minimum distance of additive quantum codes
Bounds on [[121,86]]2
lower bound: | 7 |
upper bound: | 10 |
Construction
Construction of a [[121,86,7]] quantum code:
[1]: [[256, 222, 7]] quantum code over GF(2^2)
Extended BCH code with parameters 255 6
[2]: [[120, 86, 7]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 5, 6, 9, 11, 14, 16, 18, 19, 20, 21, 22, 23, 26, 27, 31, 33, 34, 35, 38, 39, 40, 43, 44, 46, 47, 51, 60, 66, 71, 72, 73, 74, 75, 77, 78, 79, 80, 82, 83, 88, 89, 90, 93, 94, 96, 101, 106, 108, 110, 115, 117, 119, 120, 122, 124, 127, 128, 129, 130, 132, 135, 137, 139, 141, 143, 144, 146, 147, 148, 149, 151, 153, 156, 157, 159, 160, 162, 166, 167, 168, 173, 176, 177, 178, 179, 180, 182, 183, 185, 186, 187, 188, 189, 191, 195, 197, 198, 199, 200, 201, 202, 203, 204, 206, 207, 208, 209, 211, 215, 216, 217, 218, 221, 226, 227, 229, 230, 232, 233, 236, 237, 238, 239, 240, 241, 242, 244, 247, 249, 251, 252, 253, 255, 256 }
[3]: [[121, 86, 7]] 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