Bounds on the minimum distance of additive quantum codes
Bounds on [[104,56]]2
lower bound: | 9 |
upper bound: | 16 |
Construction
Construction of a [[104,56,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[104, 56, 9]] quantum code over GF(2^2)
Shortening of [1] at { 2, 3, 4, 5, 6, 7, 10, 13, 14, 16, 19, 20, 21, 26, 27, 29, 32, 34, 35, 36, 38, 41, 42, 46, 48, 50, 51, 52, 54, 55, 59, 62, 65, 66, 70, 71, 72, 76, 78, 79, 80, 81, 82, 84, 86, 87, 88, 90, 91, 93, 94, 95, 96, 97, 98, 99, 100, 104, 105, 106, 108, 110, 112, 113, 114, 115, 116, 119, 120, 121, 122, 124, 126, 127, 129, 130, 131, 132, 134, 138, 139, 140, 143, 144, 145, 146, 151, 152, 154, 155, 156, 158, 161, 162, 163, 164, 165, 166, 167, 169, 170, 171, 174, 175, 181, 185, 187, 189, 190, 191, 193, 194, 195, 196, 197, 198, 199, 202, 205, 209, 211, 212, 213, 214, 215, 216, 218, 219, 221, 222, 223, 225, 231, 232, 233, 235, 236, 237, 239, 241, 242, 243, 244, 245, 246, 247, 249, 250, 251, 254, 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 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 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 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0]
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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