Bounds on the minimum distance of additive quantum codes
Bounds on [[138,108]]2
| lower bound: | 6 |
| upper bound: | 8 |
Construction
Construction of a [[138,108,6]] quantum code:
[1]: [[256, 230, 6]] quantum code over GF(2^2)
Extended BCH code with parameters 255 5
[2]: [[138, 112, 6]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 6, 7, 8, 11, 17, 18, 20, 24, 27, 28, 32, 36, 37, 38, 40, 41, 43, 45, 48, 51, 53, 55, 58, 59, 60, 61, 63, 65, 68, 70, 73, 74, 75, 82, 85, 86, 89, 90, 93, 95, 96, 98, 101, 102, 103, 105, 106, 107, 108, 116, 118, 119, 123, 127, 129, 132, 134, 135, 136, 142, 143, 144, 145, 147, 148, 150, 153, 157, 160, 164, 165, 166, 169, 171, 172, 173, 175, 178, 183, 185, 186, 191, 192, 195, 196, 198, 201, 203, 204, 205, 207, 210, 211, 213, 214, 216, 217, 218, 223, 225, 227, 228, 232, 233, 236, 240, 242, 243, 245, 246, 248, 250, 251, 253, 255, 256 }
[3]: [[138, 108, 6]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
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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