Bounds on the minimum distance of additive quantum codes
Bounds on [[135,88]]2
| lower bound: | 8 |
| upper bound: | 14 |
Construction
Construction of a [[135,88,8]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[136, 88, 9]] quantum code over GF(2^2)
Shortening of [1] at { 9, 40, 45, 48, 50, 51, 52, 53, 55, 56, 59, 61, 64, 65, 66, 67, 70, 73, 74, 76, 77, 78, 80, 82, 83, 85, 88, 89, 90, 93, 94, 95, 98, 103, 106, 108, 109, 111, 112, 113, 115, 117, 118, 119, 120, 121, 123, 124, 126, 129, 130, 133, 134, 135, 136, 137, 139, 141, 142, 148, 149, 153, 154, 155, 160, 164, 165, 166, 168, 170, 171, 173, 174, 175, 176, 177, 179, 180, 182, 183, 186, 187, 189, 191, 198, 199, 200, 203, 204, 205, 207, 209, 211, 212, 213, 214, 215, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 229, 230, 232, 235, 236, 237, 239, 240, 243, 250, 252, 254 }
[3]: [[135, 89, 8]] quantum code over GF(2^2)
Shortening of the stabilizer code of [2] at { 136 }
[4]: [[135, 88, 8]] quantum code over GF(2^2)
Subcode of [3]
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 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1|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 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 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