Bounds on the minimum distance of additive quantum codes
Bounds on [[121,73]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[121,73,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[121, 73, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 14, 17, 18, 19, 20, 25, 28, 29, 30, 31, 35, 37, 38, 42, 44, 47, 48, 50, 52, 53, 54, 55, 57, 63, 64, 66, 67, 68, 69, 70, 71, 72, 74, 75, 81, 83, 84, 88, 90, 91, 99, 100, 104, 105, 107, 108, 109, 110, 111, 113, 114, 116, 120, 124, 125, 126, 128, 129, 130, 131, 133, 135, 138, 141, 142, 145, 147, 148, 149, 151, 152, 154, 155, 156, 157, 165, 166, 170, 171, 173, 175, 176, 178, 179, 184, 187, 188, 189, 190, 192, 196, 197, 198, 199, 200, 203, 204, 205, 206, 211, 212, 215, 217, 218, 221, 222, 224, 227, 228, 229, 235, 237, 239, 240, 241, 242, 243, 244, 246, 247, 250, 251, 252, 254 }
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 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 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