Bounds on the minimum distance of additive quantum codes
Bounds on [[136,50]]2
| lower bound: | 15 |
| upper bound: | 28 |
Construction
Construction of a [[136,50,15]] quantum code:
[1]: [[256, 174, 15]] quantum code over GF(2^2)
Extended BCH code with parameters 255 14
[2]: [[136, 54, 15]] quantum code over GF(2^2)
Shortening of [1] at { 1, 3, 4, 6, 7, 8, 9, 10, 11, 13, 15, 25, 29, 32, 36, 40, 41, 42, 45, 47, 49, 50, 52, 61, 62, 64, 68, 70, 73, 76, 82, 83, 84, 85, 86, 88, 89, 90, 93, 94, 95, 99, 100, 102, 105, 106, 107, 111, 113, 114, 115, 116, 122, 123, 125, 126, 128, 131, 136, 141, 142, 143, 144, 147, 148, 149, 150, 151, 153, 155, 156, 157, 158, 159, 160, 162, 167, 169, 171, 172, 173, 174, 178, 179, 180, 182, 185, 186, 188, 189, 193, 194, 197, 199, 203, 204, 205, 209, 210, 211, 214, 218, 223, 224, 225, 230, 232, 234, 237, 238, 239, 240, 243, 248, 249, 250, 251, 252, 254, 256 }
[3]: [[136, 50, 15]] quantum code over GF(2^2)
Subcode of [2]
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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 0 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 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1]
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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.
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Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024