Bounds on the minimum distance of additive quantum codes
Bounds on [[103,54]]2
lower bound: | 9 |
upper bound: | 16 |
Construction
Construction of a [[103,54,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[102, 54, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 3, 5, 8, 9, 10, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 25, 28, 30, 31, 32, 33, 35, 40, 41, 46, 47, 48, 49, 50, 52, 54, 55, 56, 58, 60, 61, 62, 65, 66, 67, 71, 73, 74, 75, 76, 78, 80, 81, 83, 86, 87, 88, 89, 90, 92, 93, 95, 96, 97, 100, 101, 102, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 119, 122, 123, 124, 125, 127, 128, 129, 130, 132, 133, 134, 135, 136, 137, 139, 142, 144, 145, 146, 147, 149, 150, 151, 152, 153, 155, 157, 160, 161, 168, 169, 170, 171, 172, 174, 176, 178, 179, 181, 183, 185, 186, 189, 192, 194, 196, 198, 202, 203, 204, 205, 206, 209, 211, 213, 214, 215, 217, 218, 219, 220, 221, 223, 225, 227, 228, 229, 232, 233, 234, 238, 240, 244, 246, 247, 248, 249, 251, 252 }
[3]: [[103, 54, 9]] quantum code over GF(2^2)
ExtendCode [2] by 1
stabilizer matrix:
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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