Bounds on the minimum distance of additive quantum codes
Bounds on [[119,70]]2
lower bound: | 9 |
upper bound: | 15 |
Construction
Construction of a [[119,70,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[118, 70, 9]] quantum code over GF(2^2)
Shortening of [1] at { 2, 8, 10, 11, 12, 13, 14, 16, 18, 20, 22, 25, 26, 30, 31, 32, 36, 37, 38, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 62, 64, 66, 69, 70, 71, 73, 74, 76, 78, 80, 84, 85, 90, 91, 92, 95, 99, 100, 103, 105, 106, 107, 110, 112, 113, 120, 122, 123, 124, 127, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 146, 148, 149, 153, 154, 155, 161, 162, 163, 164, 165, 167, 169, 172, 173, 174, 181, 182, 183, 184, 187, 188, 189, 190, 195, 197, 199, 201, 203, 204, 207, 208, 210, 215, 217, 219, 220, 221, 222, 224, 225, 227, 228, 230, 233, 234, 235, 237, 238, 240, 243, 244, 246, 247, 249, 253, 255 }
[3]: [[119, 70, 9]] quantum code over GF(2^2)
ExtendCode [2] 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 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 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 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1 1 1 0 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 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 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 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 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 1 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 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 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 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 0 0 0 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 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 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 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 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 1 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 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 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 0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 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 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 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 1 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 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 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 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 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 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 1 0 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 1 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 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 0 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 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 0 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 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 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 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 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 0 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 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 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 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 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 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 1 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 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 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 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 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 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 1 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 1 0 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 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 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 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 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 1 1 0 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 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 1 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 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 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 1 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 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 1 1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 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 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 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 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 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 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 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 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 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 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 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 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 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 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 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 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 1 0 1 0 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 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 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 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1 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 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 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 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 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 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 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 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 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 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 1 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 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 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 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 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 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 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 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|1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 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 0 0|0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 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|0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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 1 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 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 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 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