Bounds on the minimum distance of additive quantum codes
Bounds on [[122,89]]2
lower bound: | 6 |
upper bound: | 10 |
Construction
Construction of a [[122,89,6]] quantum code:
[1]: [[168, 134, 7]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[122, 88, 7]] quantum code over GF(2^2)
Shortening of [1] at { 2, 3, 6, 8, 10, 12, 18, 20, 24, 26, 27, 32, 34, 35, 39, 42, 43, 48, 54, 56, 57, 60, 64, 66, 70, 94, 110, 111, 113, 114, 120, 122, 125, 126, 128, 129, 134, 135, 137, 141, 143, 149, 152, 155, 156, 161 }
[3]: [[121, 89, 6]] quantum code over GF(2^2)
Shortening of the stabilizer code of [2] at 122
[4]: [[122, 89, 6]] quantum code over GF(2^2)
ExtendCode [3] by 1
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 1 1 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0|0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0]
[0 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 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0]
[0 0 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 1 1 1 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0|0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0|0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0|0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 0|0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0|0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 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 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0|0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0|0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0|0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0|0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0|0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 0 0 1 1 0|0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 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 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0|0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 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 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 1 0 0|0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 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 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0|0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 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 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 0|0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 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 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 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 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 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 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0|1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 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 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 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 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 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 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 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 0 0 0 0 0 0|0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 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 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 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 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 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 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 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 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 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 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 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 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 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 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 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 0 0 0 0 0 0|0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 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 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 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 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0]
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