Bounds on the minimum distance of additive quantum codes
Bounds on [[119,47]]2
lower bound: | 13 |
upper bound: | 24 |
Construction
Construction of a [[119,47,13]] quantum code:
[1]: [[255, 183, 13]] quantum code over GF(2^2)
BCH code with parameters 255 13
[2]: [[119, 47, 13]] quantum code over GF(2^2)
Shortening of [1] at { 2, 4, 8, 9, 10, 11, 12, 13, 14, 19, 22, 23, 24, 26, 29, 31, 32, 33, 34, 36, 38, 39, 42, 44, 46, 51, 52, 53, 55, 56, 62, 64, 66, 67, 68, 69, 70, 72, 78, 79, 80, 81, 83, 84, 92, 93, 94, 95, 96, 97, 98, 101, 103, 105, 106, 110, 113, 115, 116, 119, 120, 122, 123, 125, 126, 127, 129, 130, 133, 135, 136, 137, 142, 143, 144, 145, 146, 149, 150, 151, 155, 156, 157, 158, 159, 161, 162, 163, 167, 169, 174, 177, 180, 181, 182, 184, 185, 186, 196, 197, 198, 199, 200, 201, 206, 210, 212, 215, 216, 217, 218, 219, 224, 225, 226, 228, 229, 230, 231, 232, 233, 234, 235, 236, 239, 240, 242, 243, 244, 246, 247, 250, 251, 253, 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 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 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 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