Bounds on the minimum distance of additive quantum codes
Bounds on [[114,66]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[114,66,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[114, 66, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 4, 5, 7, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 28, 29, 30, 31, 32, 33, 34, 41, 42, 43, 44, 45, 48, 49, 50, 52, 53, 54, 55, 57, 60, 63, 65, 68, 70, 74, 75, 78, 79, 80, 83, 88, 90, 92, 94, 95, 96, 97, 99, 100, 101, 102, 103, 105, 108, 110, 112, 114, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 130, 133, 135, 136, 140, 141, 143, 144, 147, 148, 150, 151, 153, 161, 162, 163, 164, 165, 166, 167, 170, 171, 172, 173, 175, 176, 178, 179, 180, 181, 183, 184, 186, 190, 191, 192, 193, 194, 198, 199, 202, 209, 210, 213, 217, 218, 220, 222, 223, 224, 225, 227, 232, 233, 236, 240, 241, 242, 243, 246, 247, 248, 250, 251, 252, 254, 255 }
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