Bounds on the minimum distance of additive quantum codes
Bounds on [[173,104]]2
| lower bound: | 11 |
| upper bound: | 21 |
Construction
Construction of a [[173,104,11]] quantum code:
[1]: [[256, 198, 11]] quantum code over GF(2^2)
Extended BCH code with parameters 255 10
[2]: [[162, 104, 11]] quantum code over GF(2^2)
Shortening of [1] at { 3, 23, 49, 50, 53, 55, 57, 62, 67, 68, 75, 77, 79, 80, 81, 82, 83, 84, 85, 88, 89, 92, 95, 97, 99, 102, 104, 106, 107, 110, 111, 120, 123, 124, 127, 134, 136, 139, 143, 145, 146, 147, 148, 156, 158, 165, 166, 167, 169, 170, 171, 172, 173, 176, 178, 180, 182, 183, 184, 185, 186, 188, 194, 195, 196, 201, 204, 205, 206, 208, 209, 210, 211, 213, 214, 216, 220, 221, 225, 227, 228, 229, 231, 233, 235, 238, 241, 244, 246, 247, 248, 249, 250, 251 }
[3]: [[173, 104, 11]] quantum code over GF(2^2)
ExtendCode [2] by 11
stabilizer matrix:
[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 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 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