Bounds on the minimum distance of additive quantum codes
Bounds on [[127,79]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[127,79,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[127, 79, 9]] quantum code over GF(2^2)
Shortening of [1] at { 2, 4, 5, 6, 7, 8, 13, 15, 19, 20, 21, 24, 25, 29, 31, 32, 33, 37, 40, 42, 45, 49, 50, 51, 54, 58, 60, 61, 62, 63, 66, 69, 70, 72, 73, 74, 77, 79, 81, 85, 86, 87, 90, 91, 94, 95, 96, 97, 100, 101, 102, 104, 105, 108, 111, 112, 113, 114, 118, 121, 122, 124, 125, 126, 127, 130, 132, 133, 134, 140, 143, 145, 147, 148, 149, 152, 154, 156, 159, 160, 161, 162, 164, 168, 171, 172, 174, 175, 177, 183, 184, 185, 187, 189, 190, 196, 198, 199, 202, 203, 204, 206, 207, 209, 210, 211, 213, 214, 215, 220, 221, 222, 223, 225, 227, 229, 230, 233, 234, 235, 236, 238, 239, 244, 247, 250, 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 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 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