Bounds on the minimum distance of additive quantum codes
Bounds on [[100,52]]2
lower bound: | 9 |
upper bound: | 16 |
Construction
Construction of a [[100,52,9]] quantum code:
[1]: [[255, 207, 9]] quantum code over GF(2^2)
BCH code with parameters 255 9
[2]: [[100, 52, 9]] quantum code over GF(2^2)
Shortening of [1] at { 1, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 17, 18, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 42, 43, 44, 46, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 62, 64, 65, 67, 68, 69, 70, 71, 72, 77, 79, 81, 82, 84, 85, 89, 91, 92, 95, 97, 98, 99, 100, 101, 102, 103, 105, 107, 111, 112, 113, 114, 117, 118, 119, 120, 121, 122, 123, 124, 127, 132, 133, 134, 136, 137, 138, 139, 140, 141, 143, 144, 147, 154, 155, 157, 159, 160, 161, 163, 164, 166, 167, 168, 171, 173, 174, 177, 179, 180, 181, 183, 184, 187, 188, 191, 192, 193, 194, 196, 197, 200, 201, 203, 204, 206, 211, 213, 216, 217, 220, 223, 224, 225, 226, 227, 229, 231, 234, 235, 238, 239, 240, 243, 244, 245, 246, 247, 248, 249, 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 1 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 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 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 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 1 1 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 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 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 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 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 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 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 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 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 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 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 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 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 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 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 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 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 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 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 1 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 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 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 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 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 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 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 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 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 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 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 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 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 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 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 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 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 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 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 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 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 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 1 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 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 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 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 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 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 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 0 1 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 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 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 1 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 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 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 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 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 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 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 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 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 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 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 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 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 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 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 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 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 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 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 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 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 1 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 1 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 0 1 1 1 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 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 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 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 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 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 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 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 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 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 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 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 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 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 0 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 1 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 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 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 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 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|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 0 1 1 1 0 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 1 1 0 1 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1 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 1 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 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 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 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1 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 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 1 0 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