Bounds on the minimum distance of additive quantum codes
Bounds on [[122,74]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[122,74,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[122, 74, 9]] quantum code over GF(2^2)
Shortening of [1] at { 2, 3, 4, 7, 8, 9, 12, 16, 17, 18, 19, 21, 22, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 40, 42, 44, 45, 47, 49, 52, 54, 56, 58, 60, 61, 63, 64, 65, 66, 69, 70, 72, 76, 79, 81, 84, 85, 86, 87, 88, 89, 90, 93, 97, 98, 100, 102, 107, 110, 111, 113, 114, 115, 123, 124, 127, 130, 131, 134, 136, 137, 145, 147, 148, 149, 151, 154, 155, 156, 157, 159, 160, 161, 163, 164, 166, 167, 169, 172, 175, 176, 178, 182, 183, 184, 186, 188, 189, 191, 192, 197, 201, 202, 203, 204, 206, 209, 210, 212, 213, 214, 215, 216, 219, 220, 222, 223, 225, 227, 228, 235, 238, 239, 240, 247, 248, 249, 251, 252, 253 }
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