Code details
best found code with parameters
q=13 k=3 n=38
minimum distance = 34
this is new optimal code
the previous bounds were -1/34
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 25 orbits of sizes:
|
2
|
3
|
3
|
1
|
12
|
6
|
12
|
6
|
6
|
12
|
12
|
12
|
12
|
6
|
6
|
12
|
6
|
6
|
6
|
6
|
6
|
6
|
6
|
12
|
6
|
The solution of the corresponding linear system of equations was found after less than 10 seconds:
|
1
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
4
|
4
|
2
|
4
|
1
|
4
|
3
|
4
|
3
|
2
|
4
|
0
|
0
|
4
|
4
|
4
|
0
|
3
|
1
|
4
|
4
|
4
|
4
|
2
|
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
|
|
0
|
12
|
12
|
1
|
4
|
2
|
9
|
5
|
11
|
3
|
8
|
10
|
7
|
6
|
12
|
4
|
2
|
8
|
10
|
6
|
12
|
4
|
2
|
8
|
10
|
6
|
1
|
9
|
5
|
11
|
3
|
7
|
1
|
9
|
5
|
11
|
3
|
7
|
|
12
|
0
|
7
|
6
|
3
|
5
|
10
|
2
|
8
|
4
|
11
|
9
|
12
|
1
|
4
|
12
|
2
|
8
|
6
|
10
|
12
|
8
|
10
|
4
|
2
|
6
|
11
|
3
|
7
|
1
|
9
|
5
|
3
|
7
|
11
|
5
|
1
|
9
|
Which is a code with the following weight distribution
1y38+1224x34y4+288x35y3+228x36y2+168x37y1+288x38