76
5 Quantum Code Constructions
Table 5.6 Code comparison
Our Hermitian Codes (Construction IV)
Hermitian Codes in [4]
[[n, k, d]] q
[[n
, k
, d
]] q
[[17, 13, 3]] 4 (MDS)
[[17, 9, 5]] 4 (MDS)
[[13, 9, 3]] 5 (MDS)
[[312, 298, d ≥ 5]] 5
[[312, 296, d
≥ 5]] 5
[[312, 294, d ≥ 6]] 5
[[312, 292, d
≥ 6]] 5
[[312, 290, d ≥ 7]] 5
[[312, 288, d
≥ 7]] 5
[[312, 286, d ≥ 8]] 5
[[312, 284, d
≥ 8]] 5
[[312, 282, d ≥ 9]] 5
[[312, 280, d
≥ 9]] 5
[[312, 278, d ≥ 10]] 5
[[312, 276, d
≥ 10]] 5
[[312, 274, d ≥ 11]] 5
[[312, 272, d
≥ 11]] 5
[[312, 270, d ≥ 12]] 5
[[312, 268, d
≥ 12]] 5
[[144, 128, d ≥ 5]] 7
[[144, 120, d ≥ 5]] 7
[[144, 122, d ≥ 6]] 7
[[144, 114, d ≥ 6]] 7
[[144, 116, d ≥ 7]] 7
[[144, 108, d ≥ 7]] 7
[[144, 114, d ≥ 8]] 7
[[144, 102, d ≥ 8]] 7
[[144, 108, d ≥ 9]] 7
[[144, 96, d ≥ 9]] 7
[[144, 102, d ≥ 10]] 7
[[144, 90, d ≥ 10]] 7
[[144, 100, d ≥ 11]] 7
[[144, 84, d ≥ 11]] 7
Table 5.7 Our quantum codes
Parameters of the new codes
[[11, 1, d ≥ 4]] 5
[[19, 1, d ≥ 5]] 17
[[35, 27, d ≥ 3]] 13
[[35, 27, d ≥ 3]] 27
[[35, 19, d ≥ 4]] 27
[[51, 35, d ≥ 3]] 32
[[61, 51, d ≥ 3]] 9
[[63, 51, d ≥ 3]] 11
[[63, 39, d ≥ 4]] 11
[[63, 51, d ≥ 3]] 23
[[63, 45, d ≥ 4]] 23
[[67, 61, d ≥ 3]] 29
[[73, 67, d ≥ 3]] 64
[[73, 61, d ≥ 4]] 64