Bounds on the minimum distance of additive quantum codes
Bounds on [[111,61]]2
| lower bound: | 9 |
| upper bound: | 16 |
Construction
Construction of a [[111,61,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[109, 61, 9]] quantum code over GF(2^2)
Shortening of [1] at { 3, 4, 5, 7, 9, 11, 12, 17, 20, 21, 22, 23, 24, 26, 28, 29, 30, 32, 33, 35, 37, 38, 41, 43, 44, 45, 46, 48, 50, 52, 53, 55, 58, 59, 60, 62, 65, 66, 67, 68, 69, 70, 74, 76, 77, 79, 81, 87, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 103, 106, 108, 110, 111, 113, 114, 117, 121, 123, 125, 129, 132, 133, 134, 135, 136, 139, 140, 143, 146, 147, 148, 150, 151, 152, 154, 155, 157, 159, 162, 163, 164, 167, 168, 170, 171, 173, 174, 175, 177, 178, 179, 180, 181, 184, 186, 187, 189, 192, 194, 195, 197, 198, 199, 200, 201, 203, 209, 213, 217, 218, 219, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 232, 234, 235, 236, 237, 238, 239, 240, 245, 246, 247, 248, 250, 251, 253 }
[3]: [[111, 61, 9]] quantum code over GF(2^2)
ExtendCode [2] by 2
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 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 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 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 1 0 0 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 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 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 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 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 0 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1 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 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 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 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 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 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 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 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 0 0 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 1 0 0 0 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 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 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 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 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 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 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 1 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 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 0 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 1 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 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 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 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 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 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 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 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 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 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 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 0 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 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 1 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 0 1 0 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 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 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 1 0 1 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 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 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 0 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 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 1 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 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 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 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 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 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 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 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 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 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 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 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 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 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 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 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 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 0 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 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 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 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 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 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 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 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 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 1 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 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 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 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 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 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 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 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 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 1 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 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 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 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 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 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 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 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 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 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 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 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 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 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 1 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 0 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 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 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 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 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 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 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 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 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 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 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 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 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 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|1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 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 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 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 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 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 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 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