Code details
best found code with parameters
q=13 k=3 n=118
minimum distance = 108
this is new optimal code
the previous bounds were -1/108
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 21 orbits of sizes:
|
3
|
6
|
4
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
6
|
12
|
4
|
12
|
6
|
12
|
4
|
6
|
6
|
6
|
The solution of the corresponding linear system of equations was found after less than 10 seconds:
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
10
|
7
|
10
|
10
|
10
|
9
|
10
|
8
|
9
|
10
|
9
|
9
|
10
|
0
|
10
|
10
|
9
|
10
|
9
|
5
|
9
|
This produces the following generator matrix
|
0
|
0
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
0
|
0
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
0
|
0
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
0
|
0
|
12
|
12
|
12
|
12
|
0
|
0
|
12
|
12
|
12
|
12
|
|
12
|
12
|
0
|
0
|
12
|
6
|
12
|
12
|
1
|
1
|
5
|
5
|
11
|
11
|
7
|
7
|
6
|
6
|
12
|
12
|
4
|
4
|
2
|
2
|
8
|
8
|
10
|
10
|
6
|
6
|
12
|
12
|
4
|
4
|
2
|
2
|
8
|
8
|
10
|
10
|
6
|
6
|
1
|
1
|
2
|
2
|
9
|
9
|
3
|
3
|
8
|
8
|
7
|
7
|
1
|
1
|
1
|
1
|
4
|
4
|
10
|
10
|
7
|
7
|
7
|
7
|
12
|
12
|
0
|
0
|
1
|
7
|
4
|
4
|
9
|
9
|
5
|
5
|
11
|
11
|
3
|
3
|
10
|
10
|
12
|
12
|
0
|
0
|
4
|
10
|
2
|
2
|
5
|
5
|
5
|
5
|
11
|
11
|
11
|
11
|
8
|
8
|
2
|
2
|
8
|
8
|
12
|
12
|
0
|
0
|
9
|
3
|
12
|
12
|
0
|
0
|
5
|
11
|
|
12
|
6
|
12
|
6
|
0
|
0
|
1
|
7
|
12
|
6
|
5
|
11
|
5
|
11
|
12
|
6
|
1
|
7
|
4
|
10
|
12
|
6
|
2
|
8
|
2
|
8
|
12
|
6
|
4
|
10
|
2
|
8
|
4
|
10
|
12
|
6
|
12
|
6
|
4
|
10
|
2
|
8
|
4
|
10
|
9
|
3
|
5
|
11
|
5
|
11
|
9
|
3
|
4
|
10
|
2
|
5
|
11
|
8
|
5
|
11
|
5
|
11
|
2
|
5
|
11
|
8
|
1
|
7
|
5
|
11
|
0
|
0
|
9
|
3
|
1
|
7
|
2
|
8
|
2
|
8
|
1
|
7
|
9
|
3
|
4
|
10
|
2
|
8
|
0
|
0
|
1
|
7
|
1
|
4
|
10
|
7
|
1
|
4
|
10
|
7
|
1
|
7
|
4
|
10
|
4
|
10
|
9
|
3
|
9
|
3
|
0
|
0
|
5
|
11
|
1
|
7
|
0
|
0
|
Which is a code with the following weight distribution
1y118+1068x108y10+792x109y9+144x110y8+72x111y7+72x113y5+48x118