Code details
best found code with parameters
q=17 k=3 n=78
minimum distance = 72
this is new optimal code
the previous bounds were -1/72
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 21 orbits of sizes:
|
3
|
12
|
12
|
24
|
24
|
24
|
12
|
24
|
24
|
12
|
24
|
24
|
12
|
12
|
12
|
12
|
12
|
4
|
12
|
6
|
6
|
The solution of the corresponding linear system of equations was found after less than 100 seconds:
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
1
|
6
|
4
|
0
|
1
|
4
|
6
|
5
|
6
|
6
|
3
|
3
|
5
|
4
|
6
|
5
|
6
|
6
|
6
|
6
|
1
|
5
|
This produces the following generator matrix
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16
|
16
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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
|
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
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
0
|
0
|
16
|
16
|
16
|
16
|
|
16
|
16
|
14
|
14
|
1
|
1
|
12
|
12
|
5
|
5
|
10
|
10
|
2
|
2
|
13
|
13
|
4
|
4
|
9
|
9
|
6
|
6
|
8
|
8
|
16
|
16
|
14
|
14
|
15
|
15
|
7
|
7
|
6
|
6
|
8
|
8
|
1
|
1
|
5
|
5
|
15
|
15
|
7
|
7
|
13
|
13
|
9
|
9
|
16
|
16
|
16
|
16
|
0
|
0
|
0
|
0
|
1
|
5
|
13
|
9
|
12
|
12
|
15
|
15
|
10
|
10
|
2
|
2
|
7
|
7
|
4
|
4
|
16
|
16
|
0
|
0
|
11
|
3
|
|
5
|
13
|
12
|
4
|
10
|
2
|
14
|
6
|
16
|
8
|
1
|
9
|
1
|
9
|
16
|
8
|
14
|
6
|
10
|
2
|
12
|
4
|
5
|
13
|
15
|
7
|
14
|
6
|
16
|
8
|
16
|
8
|
14
|
6
|
15
|
7
|
15
|
7
|
5
|
13
|
1
|
9
|
1
|
9
|
5
|
13
|
15
|
7
|
14
|
10
|
2
|
6
|
1
|
5
|
13
|
9
|
0
|
0
|
0
|
0
|
12
|
4
|
10
|
2
|
15
|
7
|
15
|
7
|
10
|
2
|
12
|
4
|
12
|
4
|
11
|
3
|
0
|
0
|
Which is a code with the following weight distribution
1y78+2128x72y6+1152x73y5+576x74y4+384x75y3+480x77y1+192x78