Bounds on the minimum distance of additive quantum codes
Bounds on [[127,41]]2
| lower bound: | 15 |
| upper bound: | 29 |
Construction
Construction of a [[127,41,15]] quantum code:
[1]: [[256, 166, 16]] quantum code over GF(2^2)
Extended BCH code with parameters 255 15
[2]: [[128, 42, 16]] quantum code over GF(2^2)
Shortening of [1] at { 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 18, 20, 21, 22, 24, 28, 33, 34, 36, 37, 41, 42, 43, 44, 47, 48, 49, 52, 53, 57, 59, 60, 62, 65, 69, 71, 74, 76, 78, 81, 82, 83, 85, 86, 87, 89, 90, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 105, 108, 109, 112, 113, 115, 117, 121, 122, 128, 129, 130, 132, 134, 136, 138, 139, 140, 141, 142, 145, 147, 152, 155, 156, 157, 158, 159, 160, 161, 162, 167, 169, 170, 171, 172, 176, 177, 179, 187, 191, 192, 193, 197, 200, 202, 203, 204, 211, 212, 215, 218, 221, 222, 224, 225, 226, 229, 235, 237, 239, 240, 242, 243, 245, 247, 248, 251, 253, 254 }
[3]: [[127, 43, 15]] quantum code over GF(2^2)
Shortening of the stabilizer code of [2] at { 128 }
[4]: [[127, 41, 15]] 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 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 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 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 1 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0]
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last modified: 2009-01-27
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 even 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: 23.10.2014