Bounds on the minimum distance of additive quantum codes
Bounds on [[115,67]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[115,67,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[115, 67, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 4, 5, 6, 8, 9, 10, 11, 13, 15, 19, 21, 25, 27, 28, 29, 30, 33, 34, 37, 38, 39, 41, 43, 44, 45, 46, 47, 48, 49, 50, 52, 57, 58, 59, 60, 61, 65, 66, 67, 69, 70, 71, 74, 76, 78, 83, 84, 88, 89, 90, 92, 93, 94, 95, 99, 103, 106, 107, 108, 111, 112, 113, 114, 115, 117, 119, 120, 121, 124, 125, 130, 133, 135, 136, 137, 139, 140, 143, 144, 149, 150, 151, 161, 162, 164, 165, 167, 169, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 188, 189, 190, 195, 196, 198, 200, 201, 202, 205, 206, 207, 210, 212, 213, 215, 222, 223, 224, 229, 230, 231, 232, 234, 235, 236, 239, 242, 244, 245, 246, 248, 250, 252, 253, 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 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 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