Bounds on the minimum distance of additive quantum codes
Bounds on [[117,69]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[117,69,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[117, 69, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 4, 5, 7, 10, 12, 16, 17, 19, 20, 22, 24, 25, 26, 27, 28, 29, 31, 32, 33, 35, 36, 38, 39, 40, 43, 44, 46, 48, 49, 50, 53, 54, 56, 57, 59, 60, 61, 65, 66, 67, 72, 75, 76, 79, 81, 83, 86, 87, 88, 89, 91, 92, 93, 95, 97, 99, 100, 105, 107, 108, 109, 110, 114, 116, 120, 123, 127, 128, 129, 131, 132, 133, 135, 137, 138, 139, 140, 142, 143, 145, 146, 147, 148, 149, 151, 152, 154, 156, 157, 158, 161, 163, 165, 169, 170, 172, 173, 175, 176, 178, 180, 182, 183, 184, 185, 188, 189, 192, 193, 196, 198, 200, 206, 209, 211, 213, 215, 218, 219, 225, 226, 227, 229, 231, 233, 234, 235, 236, 239, 241, 245, 246, 247, 249, 252, 253, 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 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 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 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 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 1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 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 0 0 0 1 1 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 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 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 0 1]
[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 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 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 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 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 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 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 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0|0 0 0 0 0 0 0 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 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 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 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 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 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 0 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 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 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 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 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 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 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 1 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 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 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 1 0 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 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 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 1 1 1 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 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 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 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 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 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 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 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 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 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 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 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 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 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 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 1 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1|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 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 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 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 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 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 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 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 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 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 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 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 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 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 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 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 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 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 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 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 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 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 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 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 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|1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 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 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 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 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 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 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 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 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 0 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 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 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 0 0 0 1 1 1 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 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