Bounds on the minimum distance of additive quantum codes
tables for
n≤30
,
n≤128
,
n≤256
n/k
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
1
1
1
2
2
1
1
3
2
1
1
1
4
2
2
2
1
1
5
3
3
2
1
1
1
6
4
3
2
2
2
1
1
7
3
3
2
2
2
1
1
1
8
4
3
3
3
2
2
2
1
1
9
4
3
3
3
2
2
2
1
1
1
10
4
4
4
3
3
2
2
2
2
1
1
11
5
5
4
3
3
3
2
2
2
1
1
1
12
6
5
4
4
4
3
3
2
2
2
2
1
1
13
5
5
4
4
4
3
3
3
2
2
2
1
1
1
14
6
5
5
4-5
4
4
4
3
3
2
2
2
2
1
1
15
6
5
5
5
4
4
4
3
3
3
2
2
2
1
1
1
16
6
6
6
5
5
4-5
4
4
3
3
3
2
2
2
2
1
1
17
7
7
6
5-6
5
4-5
4-5
4
4
4
3
3
2
2
2
1
1
1
18
8
7
6
5-6
5-6
5
5
4
4
4
3
3
2
2
2
2
2
1
1
19
7
7
6
5-6
5-6
5-6
5
4-5
4
4
3-4
3
3
2
2
2
2
1
1
1
20
8
7
6-7
6-7
6
5-6
5-6
4-5
4-5
4
4
3-4
3
3
2
2
2
2
2
1
1
21
8
7
6-7
6-7
6-7
6
5-6
5-6
4-5
4-5
4
4
3-4
3
3
3
2
2
2
1
1
1
22
8
7-8
6-8
6-7
6-7
6-7
5-6
5-6
5-6
4-5
4-5
4
4
3-4
3
3
2
2
2
2
2
1
1
23
8-9
7-9
7-8
6-8
6-7
6-7
5-7
5-6
5-6
4-6
4-5
4-5
4
4
3-4
3
3
2
2
2
2
1
1
1
24
8-10
8-9
7-8
7-8
6-8
6-7
6-7
5-7
5-6
5-6
5-6
4-5
4-5
4
4
3-4
3
3
2
2
2
2
2
1
1
25
8-9
9
7-8
7-8
7-8
7-8
6-7
5-7
5-7
5-6
5-6
4-6
4-5
4-5
4
4
3-4
3
3
2
2
2
2
1
1
1
26
8-10
9
8-9
8-9
8
7-8
6-8
6-8
6-7
5-7
5-6
5-6
5-6
4-5
4-5
4
4
3-4
3
3
2
2
2
2
2
1
1
27
9-10
9
9
9
8-9
7-8
6-8
6-8
6-8
6-7
5-7
5-6
5-6
5
4-5
4
4
4
3-4
3
3
2
2
2
2
1
1
1
28
10
10
10
9
8-9
7-9
6-8
6-8
6-8
6-8
6-7
6-7
6
5-6
5
4-5
4
4
4
3-4
3
3
2
2
2
2
2
1
1
29
11
11
10
9-10
8-9
7-9
7-9
6-8
6-8
6-8
6-7
6-7
6
5-6
5-6
4-5
4-5
4
4
4
3-4
3
3
2
2
2
2
1
1
1
30
12
11
10
9-10
8-10
8-9
7-9
7-9
7-8
6-8
6-8
6-7
6-7
5-6
5-6
5-6
5
4-5
4
4
4
3-4
3
3
2
2
2
2
2
1
1
31
10-12
11
10
9-10
8-10
8-10
7-9
7-9
7-9
7-8
6-8
6-8
6-7
5-7
5-6
5-6
5-6
5
4-5
4
4
4
3-4
3
3
2
2
2
2
1
1
1
32
10-12
11
10-11
9-11
8-10
8-10
8-10
7-10
7-9
7-9
7-8
6-8
6-8
6-7
6-7
6
6
5-6
4-5
4-5
4
4
4
3-4
3
3
2
2
2
2
2
1
1
33
10-12
11
10-11
9-11
8-11
8-10
8-10
8-10
7-10
7-9
7-9
6-8
6-8
6-8
6-7
6-7
6
5-6
4-6
4-5
4-5
4
4
4
3-4
3
3
2
2
2
2
1
1
1
34
10-12
11-12
10-12
9-11
8-11
8-11
8-10
8-10
8-10
7-10
7-9
6-9
6-8
6-8
6-8
6-7
6-7
5-6
5-6
4-6
4-5
4-5
4
4
4
3-4
3
3
2
2
2
2
2
1
1
35
11-13
11-13
10-12
9-12
9-11
8-11
8-11
8-10
8-10
7-10
7-10
7-9
7-9
7-8
6-8
6-8
6-7
5-7
5-6
5-6
5-6
4-5
4-5
4
4
4
3-4
3
3
2
2
2
2
1
1
1
36
12-14
11-13
10-12
10-12
9-12
8-11
8-11
8-11
8-11
8-10
8-10
8-10
8-9
7-9
6-8
6-8
6-8
5-7
5-7
5-6
5-6
4-6
4-5
4-5
4
4
3-4
3-4
3
3
2
2
2
2
2
1
1
37
11-14
11-13
10-12
10-12
9-12
8-12
8-11
8-11
8-11
8-11
8-10
8-10
8-10
7-9
6-8
6-8
6-8
5-7
5-7
5-6
5-6
4-6
4-6
4-5
4-5
4
3-4
3-4
3-4
3
3
2
2
2
2
1
1
1
38
12-14
11-13
10-13
10-13
9-12
8-12
8-12
8-12
8-11
8-11
8-10
8-10
8-10
7-9
6-9
6-9
6-8
6-8
6-7
5-7
5-6
5-6
5-6
4-6
4-5
4-5
4
3-4
3-4
3-4
3
3
2
2
2
2
2
1
1
39
11-14
11-13
10-13
10-13
9-13
9-12
9-12
9-12
8-12
8-11
8-11
8-10
8-10
7-10
7-9
7-9
6-8
6-8
6-8
5-7
5-7
5-6
5-6
4-6
4-6
4-5
4-5
4
3-4
3-4
3-4
3
2
2
2
2
2
1
1
1
40
12-14
11-14
10-14
10-13
10-13
10-13
10-13
9-12
8-12
8-12
8-11
8-11
8-10
7-10
7-10
7-9
6-9
6-8
6-8
6-8
6-7
5-7
5-6
5-6
5-6
4-6
4-5
4
4
4
4
3
3
3
2
2
2
2
2
1
1
41
12-15
11-15
11-14
11-14
10-13
10-13
10-13
9-13
8-12
8-12
8-12
8-11
8-11
7-10
7-10
7-10
6-9
6-9
6-8
6-8
6-8
6-7
5-7
5-6
5-6
4-6
4-5
4-5
4
4
4
4
3
3
2
2
2
2
2
1
1
1
42
12-16
12-15
12-14
11-14
10-14
10-13
10-13
9-13
9-13
8-12
8-12
8-12
8-11
7-11
7-10
7-10
7-10
7-9
7-9
7-8
7-8
6-8
6-7
5-7
5-6
5-6
5-6
4-5
4-5
4
4
4
3-4
3
3
2
2
2
2
2
2
1
1
43
13-16
13-15
12-14
11-14
10-14
10-14
10-13
9-13
9-13
8-13
8-12
8-12
8-12
8-11
8-11
7-10
7-10
7-10
7-9
7-9
7-8
6-8
6-8
5-7
5-7
5-6
5-6
4-6
4-5
4-5
4
4
3-4
3-4
3
3
2
2
2
2
2
1
1
1
44
14-16
13-15
12-15
11-15
10-14
10-14
10-14
9-14
9-13
8-13
8-12
8-12
8-12
8-12
8-11
7-11
7-10
7-10
7-10
7-9
7-9
6-8
6-8
5-8
5-7
5-7
5-6
5-6
5-6
4-5
4-5
4
4
3-4
3-4
3
3
2
2
2
2
2
2
1
1
45
13-16
13-15
12-15
11-15
10-15
10-14
10-14
9-14
9-14
9-13
8-13
8-13
8-12
8-12
8-12
8-11
8-11
7-10
7-10
7-10
7-9
6-9
6-8
6-8
5-8
5-7
5-7
5-6
5-6
5-6
4-5
4-5
4
4
3-4
3-4
3
3
2
2
2
2
2
1
1
1
46
14-16
13-16
12-16
11-15
10-15
10-15
10-15
9-14
9-14
9-14
9-13
8-13
8-12
8-12
8-12
8-11
8-11
7-11
7-10
7-10
7-10
7-9
7-8
6-8
6-8
6-8
6-7
5-6
5-6
5-6
5-6
4-5
4-5
4
4
3-4
3-4
3
3
2
2
2
2
2
2
1
1
47
13-17
13-17
12-16
11-16
10-15
10-15
10-15
10-15
9-14
9-14
9-14
8-13
8-13
8-13
8-12
8-12
8-11
7-11
7-10
7-10
7-10
7-9
7-9
7-8
6-8
6-8
6-7
5-7
5-6
5-6
5-6
4-6
4-5
4-5
4
4
3-4
3-4
3
3
2
2
2
2
2
1
1
1
48
14-18
13-17
12-16
11-16
11-16
10-15
10-15
10-15
9-15
9-14
9-14
8-14
8-14
8-13
8-12
8-12
8-12
7-11
7-11
7-10
7-10
7-10
7-9
7-9
6-8
6-8
6-8
6-7
6-7
5-6
5-6
5-6
5-6
4-5
4-5
4
4
3-4
3-4
3
3
2
2
2
2
2
2
1
1
49
13-18
13-17
12-16
12-16
11-16
11-16
10-15
10-15
9-15
9-15
9-14
9-14
8-14
8-13
8-13
8-12
8-12
7-12
7-11
7-11
7-10
7-10
7-10
7-9
6-9
6-8
6-8
6-8
6-7
5-7
5-6
5-6
5-6
4-6
4-5
4-5
4
4
3-4
3-4
3
3
2
2
2
2
2
1
1
1
50
14-18
13-17
12-17
12-17
12-16
11-16
10-16
10-16
10-15
9-15
9-15
9-14
9-14
8-14
8-13
8-13
8-12
8-12
8-12
8-11
8-11
7-10
7-10
7-10
6-9
6-9
6-8
6-8
6-8
5-7
5-7
5-6
5-6
5-6
5-6
4-5
4-5
4
4
3-4
3-4
3
3
2
2
2
2
2
2
1
1
n/k
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
This page is maintained by
Markus Grassl
(
codes@codetables.de
). Last change: 30.12.2011