Code details
best found code with parameters
q=17 k=3 n=61
minimum distance = 56
this is new optimal code
the previous bounds were -1/56
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 51 orbits of sizes:
|
1
|
2
|
8
|
1
|
4
|
2
|
8
|
2
|
8
|
2
|
8
|
2
|
8
|
2
|
8
|
1
|
4
|
4
|
4
|
4
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
2
|
8
|
8
|
8
|
8
|
2
|
4
|
4
|
4
|
8
|
8
|
8
|
The solution of the corresponding linear system of equations was found after less than 100 seconds:
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
4
|
5
|
0
|
5
|
2
|
5
|
1
|
5
|
3
|
5
|
4
|
2
|
5
|
5
|
5
|
5
|
2
|
2
|
5
|
4
|
0
|
5
|
3
|
5
|
3
|
5
|
5
|
4
|
0
|
5
|
5
|
0
|
4
|
4
|
4
|
4
|
1
|
4
|
4
|
5
|
5
|
3
|
5
|
5
|
2
|
2
|
4
|
5
|
4
|
4
|
5
|
This produces the following generator matrix
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0
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
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16
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16
|
16
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16
|
16
|
16
|
16
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16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
0
|
0
|
0
|
0
|
16
|
16
|
16
|
16
|
|
0
|
7
|
9
|
8
|
8
|
8
|
8
|
10
|
10
|
10
|
10
|
6
|
6
|
6
|
6
|
12
|
12
|
12
|
12
|
4
|
4
|
4
|
4
|
3
|
3
|
3
|
3
|
13
|
13
|
13
|
13
|
14
|
14
|
14
|
14
|
2
|
2
|
2
|
2
|
5
|
5
|
5
|
5
|
11
|
11
|
11
|
11
|
1
|
15
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
0
|
0
|
0
|
0
|
|
16
|
0
|
0
|
1
|
5
|
13
|
9
|
15
|
11
|
3
|
7
|
1
|
5
|
13
|
9
|
14
|
10
|
2
|
6
|
14
|
10
|
2
|
6
|
1
|
5
|
13
|
9
|
14
|
10
|
2
|
6
|
1
|
5
|
13
|
9
|
15
|
11
|
3
|
7
|
14
|
10
|
2
|
6
|
1
|
5
|
13
|
9
|
0
|
0
|
15
|
11
|
3
|
7
|
15
|
11
|
3
|
7
|
15
|
11
|
3
|
7
|
Which is a code with the following weight distribution
1y61+1888x56y5+1424x57y4+512x58y3+320x59y2+256x60y1+512x61