Bounds on the minimum distance of additive quantum codes
Bounds on [[112,39]]2
lower bound: | 13 |
upper bound: | 25 |
Construction
Construction of a [[112,39,13]] quantum code:
[1]: [[255, 183, 13]] quantum code over GF(2^2)
BCH code with parameters 255 13
[2]: [[111, 39, 13]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 5, 11, 17, 19, 20, 21, 22, 24, 25, 28, 32, 33, 34, 37, 38, 39, 41, 42, 43, 47, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 65, 67, 68, 69, 70, 74, 75, 76, 77, 80, 83, 85, 90, 91, 92, 94, 97, 99, 100, 101, 102, 103, 104, 105, 106, 108, 109, 110, 111, 112, 113, 118, 119, 120, 121, 123, 125, 126, 130, 131, 132, 134, 139, 141, 142, 143, 146, 147, 149, 152, 153, 154, 158, 159, 161, 162, 163, 164, 167, 168, 169, 170, 172, 173, 175, 176, 177, 178, 179, 180, 181, 184, 185, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 206, 207, 209, 212, 213, 214, 215, 219, 220, 227, 229, 231, 232, 234, 235, 237, 239, 240, 241, 242, 244, 247, 251, 254, 255 }
[3]: [[112, 39, 13]] quantum code over GF(2^2)
ExtendCode [2] by 1
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 1 1 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 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 1 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 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