Bounds on the minimum distance of additive quantum codes
Bounds on [[120,72]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[120,72,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[120, 72, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 4, 5, 8, 9, 11, 12, 13, 14, 15, 16, 17, 22, 24, 25, 28, 29, 30, 31, 33, 36, 37, 38, 41, 42, 44, 45, 46, 47, 48, 51, 53, 54, 57, 61, 62, 64, 66, 67, 69, 70, 71, 72, 75, 77, 78, 80, 83, 84, 85, 86, 90, 91, 92, 97, 99, 103, 104, 105, 107, 108, 109, 110, 113, 117, 118, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 136, 137, 139, 142, 145, 146, 149, 151, 152, 154, 156, 158, 160, 167, 168, 171, 172, 173, 176, 180, 184, 185, 187, 188, 189, 190, 191, 192, 197, 198, 199, 200, 201, 204, 205, 207, 208, 212, 215, 217, 222, 223, 227, 229, 232, 233, 234, 235, 236, 237, 240, 241, 242, 246, 250, 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 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 0 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 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 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 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 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 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 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 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 0 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 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 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 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 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 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 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 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 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 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 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 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 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 1 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 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 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 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 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 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 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 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 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 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 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 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 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 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 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 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1 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 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 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 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 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 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 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 1 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 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 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 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 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 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 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 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 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 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 1 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 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 0 0 1 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 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 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 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 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 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 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 1 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 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 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 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 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 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 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 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 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 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 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 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 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 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 1 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 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 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 0 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 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 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 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 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 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 1 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 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 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 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1]
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