files / problems / covering / compute / covering_certificate_r10_n50.json
{
"format": "binary-radius-two-syndrome-certificate-v1",
"redundancy": 10,
"length": 50,
"column_indexing": "1-based indices into witness_r10_n50.json",
"syndrome_indexing": "representations[s] represents integer syndrome s",
"representations": [
[],
[
1
],
[
2
],
[
1,
2
],
[
3
],
[
1,
3
],
[
2,
3
],
[
49,
50
],
[
21,
22
],
[
17,
18
],
[
37,
38
],
[
3,
4
],
[
44,
45
],
[
2,
4
],
[
1,
4
],
[
4
],
[
5
],
[
1,
5
],
[
2,
5
],
[
20,
22
],
[
3,
5
],
[
17,
19
],
[
37,
39
],
[
7,
8
],
[
43,
45
],
[
41,
42
],
[
10,
11
],
[
20,
21
],
[
18,
19
],
[
28,
29
],
[
12,
13
],
[
4,
5
],
[
6
],
[
1,
6
],
[
2,
6
],
[
13,
14
],
[
3,
6
],
[
24,
25
],
[
42,
44
],
[
18,
20
],
[
19,
22
],
[
15,
16
],
[
42,
45
],
[
41,
43
],
[
34,
36
],
[
9,
10
],
[
17,
20
],
[
4,
6
],
[
5,
6
],
[
23,
25
],
[
42,
43
],
[
41,
45
],
[
18,
22
],
[
17,
21
],
[
37,
40
],
[
9,
11
],
[
34,
35
],
[
48,
50
],
[
26,
29
],
[
19,
20
],
[
18,
21
],
[
12,
14
],
[
48,
49
],
[
41,
44
],
[
1,
7
],
[
7
],
[
39,
42
],
[
2,
7
],
[
40,
44
],
[
3,
7
],
[
5,
8
],
[
16,
20
],
[
40,
45
],
[
15,
18
],
[
9,
12
],
[
23,
26
],
[
24,
27
],
[
37,
41
],
[
4,
7
],
[
30,
32
],
[
40,
43
],
[
5,
7
],
[
3,
8
],
[
33,
34
],
[
2,
8
],
[
15,
19
],
[
8
],
[
1,
8
],
[
23,
27
],
[
4,
8
],
[
10,
14
],
[
39,
41
],
[
16,
21
],
[
25,
28
],
[
38,
42
],
[
24,
26
],
[
16,
18
],
[
6,
7
],
[
40,
42
],
[
11,
13
],
[
39,
44
],
[
24,
29
],
[
37,
43
],
[
10,
12
],
[
39,
45
],
[
16,
17
],
[
46,
49
],
[
33,
35
],
[
23,
28
],
[
46,
50
],
[
15,
20
],
[
30,
31
],
[
39,
43
],
[
23,
29
],
[
37,
44
],
[
47,
50
],
[
38,
45
],
[
15,
21
],
[
6,
8
],
[
9,
14
],
[
24,
28
],
[
10,
13
],
[
25,
26
],
[
40,
41
],
[
16,
19
],
[
11,
12
],
[
37,
45
],
[
33,
36
],
[
9
],
[
1,
9
],
[
2,
9
],
[
21,
29
],
[
3,
9
],
[
18,
26
],
[
32,
35
],
[
15,
23
],
[
38,
46
],
[
43,
50
],
[
19,
27
],
[
7,
12
],
[
17,
26
],
[
6,
10
],
[
43,
49
],
[
4,
9
],
[
5,
9
],
[
45,
50
],
[
32,
36
],
[
15,
24
],
[
39,
46
],
[
7,
13
],
[
18,
27
],
[
6,
11
],
[
20,
29
],
[
19,
26
],
[
44,
49
],
[
41,
48
],
[
8,
12
],
[
44,
50
],
[
21,
28
],
[
16,
25
],
[
6,
9
],
[
8,
14
],
[
4,
10
],
[
19,
29
],
[
44,
48
],
[
41,
49
],
[
31,
35
],
[
5,
11
],
[
45,
48
],
[
3,
10
],
[
21,
27
],
[
17,
28
],
[
1,
10
],
[
10
],
[
16,
23
],
[
2,
10
],
[
43,
48
],
[
20,
27
],
[
31,
36
],
[
3,
11
],
[
40,
46
],
[
2,
11
],
[
1,
11
],
[
11
],
[
4,
11
],
[
21,
26
],
[
16,
24
],
[
42,
50
],
[
42,
49
],
[
5,
10
],
[
19,
28
],
[
18,
29
],
[
39,
48
],
[
7,
9
],
[
16,
28
],
[
21,
25
],
[
5,
13
],
[
4,
12
],
[
19,
24
],
[
17,
23
],
[
2,
12
],
[
30,
35
],
[
12
],
[
1,
12
],
[
15,
26
],
[
31,
33
],
[
3,
12
],
[
41,
46
],
[
3,
13
],
[
41,
47
],
[
19,
23
],
[
17,
24
],
[
13
],
[
1,
13
],
[
2,
13
],
[
6,
14
],
[
20,
25
],
[
40,
50
],
[
5,
12
],
[
4,
13
],
[
38,
48
],
[
30,
36
],
[
40,
49
],
[
15,
27
],
[
40,
48
],
[
8,
11
],
[
38,
49
],
[
19,
25
],
[
43,
46
],
[
16,
26
],
[
21,
24
],
[
5,
14
],
[
37,
49
],
[
20,
23
],
[
6,
12
],
[
15,
28
],
[
7,
10
],
[
32,
33
],
[
22,
24
],
[
37,
50
],
[
44,
46
],
[
30,
34
],
[
21,
23
],
[
3,
14
],
[
6,
13
],
[
2,
14
],
[
1,
14
],
[
14
],
[
4,
14
],
[
39,
50
],
[
22,
23
],
[
8,
10
],
[
45,
46
],
[
20,
24
],
[
39,
49
],
[
18,
25
],
[
15
],
[
1,
15
],
[
2,
15
],
[
8,
19
],
[
3,
15
],
[
32,
43
],
[
12,
26
],
[
9,
23
],
[
7,
18
],
[
6,
16
],
[
35,
50
],
[
13,
27
],
[
33,
46
],
[
35,
49
],
[
31,
41
],
[
4,
15
],
[
5,
15
],
[
32,
44
],
[
33,
47
],
[
9,
24
],
[
7,
19
],
[
12,
27
],
[
8,
17
],
[
31,
42
],
[
13,
26
],
[
36,
49
],
[
30,
40
],
[
10,
25
],
[
14,
28
],
[
32,
45
],
[
36,
50
],
[
8,
18
],
[
6,
15
],
[
12,
28
],
[
13,
29
],
[
8,
21
],
[
11,
24
],
[
31,
43
],
[
4,
16
],
[
36,
48
],
[
1,
16
],
[
16
],
[
10,
23
],
[
2,
16
],
[
30,
37
],
[
3,
16
],
[
32,
41
],
[
7,
20
],
[
11,
23
],
[
31,
44
],
[
34,
50
],
[
35,
48
],
[
7,
21
],
[
34,
49
],
[
9,
25
],
[
32,
42
],
[
8,
20
],
[
5,
16
],
[
30,
39
],
[
14,
26
],
[
7,
22
],
[
31,
45
],
[
10,
24
],
[
13,
28
],
[
17
],
[
1,
17
],
[
2,
17
],
[
31,
37
],
[
3,
17
],
[
5,
19
],
[
4,
18
],
[
13,
24
],
[
1,
18
],
[
18
],
[
30,
43
],
[
2,
18
],
[
9,
26
],
[
3,
18
],
[
6,
20
],
[
4,
17
],
[
5,
17
],
[
3,
19
],
[
30,
45
],
[
13,
23
],
[
1,
19
],
[
19
],
[
8,
15
],
[
2,
19
],
[
33,
48
],
[
5,
18
],
[
4,
19
],
[
10,
29
],
[
11,
28
],
[
6,
22
],
[
30,
44
],
[
9,
27
],
[
6,
17
],
[
4,
20
],
[
13,
25
],
[
32,
37
],
[
14,
24
],
[
5,
21
],
[
33,
49
],
[
35,
46
],
[
7,
16
],
[
6,
18
],
[
3,
20
],
[
9,
28
],
[
2,
20
],
[
5,
22
],
[
20
],
[
1,
20
],
[
14,
23
],
[
3,
21
],
[
4,
22
],
[
36,
46
],
[
1,
21
],
[
21
],
[
9,
29
],
[
2,
21
],
[
30,
42
],
[
3,
22
],
[
4,
21
],
[
11,
26
],
[
1,
22
],
[
22
],
[
5,
20
],
[
2,
22
],
[
9,
15
],
[
13,
19
],
[
14,
21
],
[
3,
23
],
[
10,
16
],
[
2,
23
],
[
1,
23
],
[
23
],
[
4,
23
],
[
8,
27
],
[
12,
17
],
[
32,
49
],
[
32,
50
],
[
7,
26
],
[
33,
37
],
[
36,
45
],
[
34,
41
],
[
2,
24
],
[
1,
24
],
[
24
],
[
13,
17
],
[
31,
48
],
[
6,
25
],
[
3,
24
],
[
33,
39
],
[
14,
20
],
[
8,
26
],
[
35,
45
],
[
4,
24
],
[
13,
18
],
[
7,
27
],
[
12,
19
],
[
8,
29
],
[
13,
21
],
[
14,
19
],
[
34,
45
],
[
12,
20
],
[
36,
42
],
[
5,
25
],
[
6,
23
],
[
35,
41
],
[
9,
16
],
[
7,
28
],
[
31,
49
],
[
31,
50
],
[
10,
15
],
[
30,
46
],
[
34,
44
],
[
30,
47
],
[
35,
42
],
[
3,
25
],
[
6,
24
],
[
2,
25
],
[
32,
48
],
[
25
],
[
1,
25
],
[
33,
40
],
[
4,
25
],
[
13,
20
],
[
34,
43
],
[
36,
41
],
[
8,
28
],
[
14,
18
],
[
12,
21
],
[
9,
17
],
[
31,
46
],
[
11,
21
],
[
4,
26
],
[
30,
49
],
[
8,
24
],
[
7,
23
],
[
36,
40
],
[
3,
26
],
[
9,
18
],
[
11,
22
],
[
6,
28
],
[
26
],
[
1,
26
],
[
2,
26
],
[
5,
27
],
[
4,
27
],
[
8,
23
],
[
7,
24
],
[
35,
40
],
[
13,
15
],
[
9,
19
],
[
6,
29
],
[
34,
38
],
[
10,
21
],
[
11,
20
],
[
33,
42
],
[
3,
27
],
[
5,
26
],
[
2,
27
],
[
1,
27
],
[
27
],
[
8,
25
],
[
32,
46
],
[
11,
19
],
[
12,
16
],
[
4,
28
],
[
35,
37
],
[
5,
29
],
[
36,
39
],
[
33,
43
],
[
2,
28
],
[
1,
28
],
[
28
],
[
6,
26
],
[
10,
17
],
[
9,
20
],
[
3,
28
],
[
33,
45
],
[
36,
37
],
[
3,
29
],
[
35,
39
],
[
2,
29
],
[
9,
21
],
[
29
],
[
1,
29
],
[
10,
19
],
[
4,
29
],
[
30,
48
],
[
5,
28
],
[
33,
44
],
[
9,
22
],
[
11,
18
],
[
6,
27
],
[
22,
45
],
[
7,
31
],
[
19,
42
],
[
15,
37
],
[
21,
44
],
[
14,
36
],
[
23,
46
],
[
18,
41
],
[
21,
45
],
[
15,
38
],
[
13,
34
],
[
20,
43
],
[
22,
44
],
[
9,
33
],
[
17,
41
],
[
6,
30
],
[
21,
43
],
[
14,
35
],
[
24,
46
],
[
20,
45
],
[
12,
34
],
[
15,
39
],
[
8,
31
],
[
17,
42
],
[
22,
43
],
[
26,
48
],
[
29,
50
],
[
19,
41
],
[
16,
40
],
[
29,
49
],
[
18,
42
],
[
20,
44
],
[
4,
30
],
[
7,
32
],
[
21,
42
],
[
29,
48
],
[
19,
44
],
[
17,
43
],
[
13,
36
],
[
26,
49
],
[
19,
45
],
[
14,
34
],
[
16,
37
],
[
3,
30
],
[
12,
35
],
[
2,
30
],
[
1,
30
],
[
30
],
[
19,
43
],
[
17,
44
],
[
13,
35
],
[
22,
41
],
[
18,
45
],
[
15,
40
],
[
8,
32
],
[
25,
46
],
[
12,
36
],
[
20,
42
],
[
11,
33
],
[
21,
41
],
[
16,
39
],
[
17,
45
],
[
28,
48
],
[
5,
30
],
[
31
],
[
1,
31
],
[
2,
31
],
[
17,
37
],
[
3,
31
],
[
11,
36
],
[
24,
48
],
[
12,
33
],
[
22,
40
],
[
17,
38
],
[
18,
37
],
[
10,
35
],
[
16,
43
],
[
26,
46
],
[
15,
41
],
[
4,
31
],
[
5,
31
],
[
11,
35
],
[
23,
48
],
[
26,
47
],
[
16,
45
],
[
17,
39
],
[
19,
37
],
[
15,
42
],
[
16,
44
],
[
13,
33
],
[
25,
50
],
[
20,
40
],
[
18,
39
],
[
25,
49
],
[
9,
34
],
[
10,
36
],
[
32
],
[
1,
32
],
[
2,
32
],
[
25,
48
],
[
3,
32
],
[
15,
43
],
[
9,
35
],
[
16,
41
],
[
22,
39
],
[
11,
34
],
[
28,
46
],
[
23,
50
],
[
23,
49
],
[
20,
37
],
[
7,
30
],
[
4,
32
],
[
5,
32
],
[
15,
44
],
[
9,
36
],
[
10,
34
],
[
22,
38
],
[
17,
40
],
[
21,
37
],
[
29,
46
],
[
24,
49
],
[
8,
30
],
[
14,
33
],
[
20,
39
],
[
18,
40
],
[
15,
45
],
[
16,
42
],
[
24,
50
],
[
19,
48
],
[
15,
46
],
[
4,
33
],
[
25,
40
],
[
23,
37
],
[
20,
49
],
[
24,
39
],
[
29,
44
],
[
8,
34
],
[
3,
33
],
[
12,
31
],
[
29,
45
],
[
1,
33
],
[
33
],
[
23,
38
],
[
2,
33
],
[
24,
37
],
[
22,
50
],
[
23,
39
],
[
29,
43
],
[
13,
31
],
[
17,
48
],
[
22,
49
],
[
14,
32
],
[
11,
30
],
[
21,
50
],
[
24,
38
],
[
26,
42
],
[
18,
48
],
[
5,
33
],
[
21,
49
],
[
7,
34
],
[
21,
48
],
[
29,
42
],
[
18,
49
],
[
25,
39
],
[
8,
36
],
[
18,
50
],
[
24,
40
],
[
7,
35
],
[
16,
46
],
[
26,
43
],
[
12,
32
],
[
17,
49
],
[
17,
50
],
[
6,
33
],
[
27,
44
],
[
9,
30
],
[
8,
35
],
[
26,
45
],
[
23,
40
],
[
7,
36
],
[
13,
32
],
[
25,
37
],
[
16,
47
],
[
14,
31
],
[
29,
41
],
[
19,
50
],
[
27,
43
],
[
20,
48
],
[
28,
42
],
[
26,
44
],
[
19,
49
],
[
25,
38
],
[
9,
31
],
[
17,
46
],
[
16,
49
],
[
29,
40
],
[
24,
42
],
[
16,
50
],
[
6,
35
],
[
25,
44
],
[
18,
46
],
[
23,
41
],
[
19,
47
],
[
25,
45
],
[
7,
33
],
[
10,
32
],
[
5,
34
],
[
26,
37
],
[
23,
42
],
[
4,
34
],
[
6,
36
],
[
25,
43
],
[
19,
46
],
[
15,
48
],
[
18,
47
],
[
11,
32
],
[
14,
30
],
[
26,
39
],
[
3,
34
],
[
8,
33
],
[
2,
34
],
[
24,
41
],
[
34
],
[
1,
34
],
[
9,
32
],
[
25,
42
],
[
3,
35
],
[
29,
39
],
[
2,
35
],
[
12,
30
],
[
35
],
[
1,
35
],
[
28,
37
],
[
4,
35
],
[
21,
47
],
[
15,
49
],
[
15,
50
],
[
10,
31
],
[
24,
45
],
[
20,
46
],
[
2,
36
],
[
20,
47
],
[
36
],
[
1,
36
],
[
21,
46
],
[
29,
37
],
[
3,
36
],
[
11,
31
],
[
25,
41
],
[
26,
40
],
[
23,
45
],
[
13,
30
],
[
16,
48
],
[
4,
36
],
[
6,
34
],
[
29,
38
],
[
17,
31
],
[
2,
37
],
[
1,
37
],
[
37
],
[
29,
36
],
[
5,
39
],
[
4,
38
],
[
3,
37
],
[
1,
38
],
[
38
],
[
23,
33
],
[
2,
38
],
[
4,
37
],
[
3,
38
],
[
20,
32
],
[
7,
41
],
[
29,
35
],
[
3,
39
],
[
26,
34
],
[
5,
37
],
[
1,
39
],
[
39
],
[
7,
42
],
[
2,
39
],
[
8,
41
],
[
5,
38
],
[
4,
39
],
[
14,
50
],
[
14,
49
],
[
22,
32
],
[
24,
33
],
[
9,
47
],
[
17,
32
],
[
12,
49
],
[
14,
48
],
[
6,
37
],
[
7,
43
],
[
5,
40
],
[
12,
50
],
[
8,
44
],
[
11,
47
],
[
6,
38
],
[
26,
35
],
[
8,
45
],
[
10,
46
],
[
27,
36
],
[
20,
31
],
[
15,
30
],
[
7,
44
],
[
3,
40
],
[
10,
47
],
[
8,
43
],
[
1,
40
],
[
40
],
[
11,
46
],
[
2,
40
],
[
13,
50
],
[
27,
35
],
[
4,
40
],
[
25,
33
],
[
7,
45
],
[
22,
31
],
[
26,
36
],
[
13,
49
],
[
15,
31
],
[
4,
41
],
[
7,
37
],
[
8,
39
],
[
25,
36
],
[
6,
43
],
[
10,
49
],
[
5,
42
],
[
7,
38
],
[
16,
32
],
[
3,
41
],
[
12,
46
],
[
2,
41
],
[
24,
34
],
[
41
],
[
1,
41
],
[
25,
35
],
[
6,
44
],
[
22,
30
],
[
3,
42
],
[
7,
39
],
[
2,
42
],
[
1,
42
],
[
42
],
[
4,
42
],
[
23,
34
],
[
21,
30
],
[
11,
50
],
[
11,
49
],
[
6,
45
],
[
5,
41
],
[
8,
38
],
[
15,
32
],
[
3,
43
],
[
11,
48
],
[
8,
40
],
[
1,
43
],
[
43
],
[
18,
30
],
[
2,
43
],
[
14,
47
],
[
16,
31
],
[
4,
43
],
[
9,
49
],
[
9,
50
],
[
5,
45
],
[
6,
41
],
[
17,
30
],
[
1,
44
],
[
44
],
[
4,
45
],
[
2,
44
],
[
7,
40
],
[
3,
44
],
[
14,
46
],
[
6,
42
],
[
10,
48
],
[
3,
45
],
[
19,
30
],
[
29,
33
],
[
1,
45
],
[
45
],
[
4,
44
],
[
2,
45
],
[
1,
46
],
[
46
],
[
11,
40
],
[
2,
46
],
[
12,
41
],
[
3,
46
],
[
14,
44
],
[
21,
36
],
[
20,
35
],
[
9,
38
],
[
14,
45
],
[
19,
34
],
[
26,
31
],
[
15,
33
],
[
4,
46
],
[
5,
47
],
[
4,
47
],
[
5,
46
],
[
14,
43
],
[
21,
35
],
[
7,
48
],
[
9,
39
],
[
29,
32
],
[
18,
34
],
[
10,
40
],
[
25,
30
],
[
13,
41
],
[
3,
47
],
[
20,
36
],
[
2,
47
],
[
1,
47
],
[
47
],
[
14,
42
],
[
6,
46
],
[
11,
39
],
[
22,
34
],
[
10,
38
],
[
13,
44
],
[
17,
35
],
[
19,
36
],
[
23,
30
],
[
13,
45
],
[
7,
49
],
[
21,
34
],
[
26,
32
],
[
7,
50
],
[
10,
37
],
[
12,
43
],
[
20,
34
],
[
13,
43
],
[
17,
36
],
[
19,
35
],
[
11,
37
],
[
9,
40
],
[
29,
31
],
[
12,
45
],
[
10,
39
],
[
14,
41
],
[
8,
50
],
[
12,
44
],
[
24,
30
],
[
8,
49
],
[
11,
38
],
[
6,
47
],
[
7,
46
],
[
13,
39
],
[
14,
40
],
[
12,
38
],
[
18,
33
],
[
5,
48
],
[
11,
44
],
[
23,
31
],
[
10,
43
],
[
8,
47
],
[
11,
45
],
[
6,
49
],
[
6,
50
],
[
17,
33
],
[
9,
41
],
[
16,
35
],
[
10,
45
],
[
3,
48
],
[
11,
43
],
[
24,
31
],
[
1,
48
],
[
48
],
[
25,
32
],
[
2,
48
],
[
19,
33
],
[
29,
30
],
[
4,
48
],
[
16,
36
],
[
10,
44
],
[
13,
38
],
[
7,
47
],
[
12,
39
],
[
11,
42
],
[
13,
40
],
[
14,
39
],
[
4,
50
],
[
4,
49
],
[
9,
43
],
[
15,
35
],
[
23,
32
],
[
3,
50
],
[
2,
49
],
[
1,
49
],
[
49
],
[
50
],
[
1,
50
],
[
2,
50
],
[
3,
49
],
[
22,
33
],
[
9,
44
],
[
15,
36
],
[
24,
32
],
[
14,
37
],
[
6,
48
],
[
25,
31
],
[
16,
34
],
[
21,
33
],
[
11,
41
],
[
10,
42
],
[
5,
49
],
[
5,
50
],
[
9,
45
],
[
14,
38
],
[
12,
40
]
]
}