Bounds on the minimum distance of additive quantum codes
Bounds on [[163,124]]2
| lower bound: | 7 |
| upper bound: | 11 |
Construction
Construction of a [[163,124,7]] quantum code:
[1]: [[256, 222, 7]] quantum code over GF(2^2)
Extended BCH code with parameters 255 6
[2]: [[158, 124, 7]] quantum code over GF(2^2)
Shortening of [1] at { 2, 9, 11, 22, 24, 29, 40, 43, 45, 54, 56, 59, 61, 62, 68, 71, 72, 78, 83, 86, 90, 94, 100, 107, 115, 125, 126, 127, 130, 131, 133, 134, 136, 137, 138, 139, 140, 142, 143, 145, 147, 148, 152, 153, 154, 156, 159, 161, 163, 164, 166, 170, 175, 177, 178, 181, 182, 186, 187, 188, 189, 191, 193, 195, 196, 197, 198, 200, 202, 204, 206, 207, 208, 209, 211, 214, 215, 217, 218, 219, 221, 223, 226, 228, 229, 234, 237, 238, 240, 241, 243, 244, 247, 248, 249, 251, 253, 254 }
[3]: [[163, 124, 7]] quantum code over GF(2^2)
ExtendCode [2] by 5
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 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 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0]
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last modified: 2009-02-08
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 necessarily 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: 10.06.2024