5.2 BCH Codes—Part II
75
Table 5.3 Code comparison
Our CSS codes
CSS codes in [4]
[[n, k, d]] q
[[n
, k
, d
]] q
[[11, 1, d ≥ 4]] 3
—
[[13, 1, d ≥ 4]] 3
—
[[1093, 1079, d ≥ 3]] 3
[[1093, 1065, d
≥ 3]] 3
[[31, 19, d ≥ 4]] 5
[[31, 13, d
≥ 4]] 5
[[31, 13, d ≥ 5]] 5
[[31, 7, d
≥ 5]] 5
[[71, 61, d ≥ 3]] 5
[[71, 51, d
≥ 3]] 5
[[71, 51, d ≥ 4]] 5
[[71, 41, d
≥ 4]] 5
[[73, 61, d ≥ 4]] 8
[[73, 55, d
≥ 4]] 8
[[73, 55, d ≥ 5]] 8
[[73, 49, d
≥ 5]] 8
[[73, 49, d ≥ 6]] 8
[[73, 43, d
≥ 6]] 8
[[73, 43, d ≥ 7]] 8
[[73, 37, d
≥ 7]] 8
Table 5.4 Code comparison
Our CSS codes
Steane’s code construction
[[n, k, d]] q
[[n
, k
, d
]] q : L , L
[[31, 19, d ≥ 4]] 5
[[31, 16, d
≥ 4]] 5 : [31, 22, 4] 5 , [31, 25, 3] 5
[[31, 13, d ≥ 5]] 5
[[31, 10, d
≥ 5]] 5 : [31, 19, 5] 5 , [31, 22, 4] 5
[[73, 61, d ≥ 4]] 8
[[73, 58, d
≥ 4]] 8 : [73, 64, 4] 8 , [73, 67, 3] 8
[[73, 55, d ≥ 5]] 8
[[73, 52, d
≥ 5]] 8 : [73, 61, 5] 8 , [73, 64, 4] 8
[[73, 49, d ≥ 6]] 8
[[73, 46, d
≥ 6]] 8 : [73, 58, 6] 8 , [73, 61, 5] 8
[[73, 43, d ≥ 7]] 8
[[73, 40, d
≥ 7]] 8 : [73, 55, 7] 8 , [73, 58, 6] 8
Table 5.5 Code comparison
Our codes (Construction III)
Steane’s code construction
[[n, k, d]] q
[[n
, k
, d
]] q
[[31, 22, d ≥ 4]] 5
[[31, 16, d
≥ 4]] 5
[[31, 16, d ≥ 5]] 5
[[31, 10, d
≥ 5]] 5
[[71, 56, d ≥ 4]] 5
[[71, 46, d
≥ 4]] 5
[[73, 64, d ≥ 4]] 8
[[73, 58, d
≥ 4]] 8
[[73, 58, d ≥ 5]] 8
[[73, 52, d
≥ 5]] 8
[[40, 36, 3]] 9 (MDS)
[[60, 56, 3]] 11 (MDS)