Bounds on the minimum distance of additive quantum codes
Bounds on [[111,63]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[111,63,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[111, 63, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 3, 4, 6, 8, 10, 11, 12, 14, 15, 17, 21, 22, 23, 24, 27, 29, 30, 31, 33, 37, 38, 40, 42, 43, 44, 46, 47, 48, 49, 51, 53, 55, 58, 62, 64, 65, 69, 70, 75, 77, 78, 79, 80, 81, 85, 89, 90, 91, 93, 95, 96, 99, 101, 102, 104, 106, 108, 110, 113, 114, 118, 119, 120, 121, 123, 124, 125, 126, 128, 130, 132, 133, 134, 135, 136, 137, 138, 139, 143, 146, 148, 149, 152, 153, 154, 155, 156, 157, 160, 164, 168, 170, 175, 178, 179, 180, 181, 183, 187, 188, 189, 190, 193, 194, 195, 197, 198, 201, 202, 203, 204, 207, 209, 210, 211, 213, 214, 215, 216, 218, 219, 222, 224, 225, 227, 228, 230, 232, 234, 235, 238, 239, 241, 242, 243, 244, 245, 248, 249, 250, 252, 255 }
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 1 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1]
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last modified: 2006-04-03
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