Code details
best found code with parameters
q=13 k=3 n=14
minimum distance = 12
this is new optimal code
the previous bounds were -1/12
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 15 orbits of sizes:
|
14
|
14
|
14
|
7
|
14
|
14
|
14
|
14
|
14
|
7
|
14
|
14
|
14
|
14
|
1
|
The solution of the corresponding linear system of equations was found after less than 10 seconds:
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
2
|
0
|
2
|
2
|
0
|
1
|
0
|
0
|
2
|
2
|
2
|
2
|
0
|
0
|
0
|
This produces the following generator matrix
|
0
|
0
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
|
12
|
12
|
0
|
0
|
12
|
12
|
1
|
1
|
4
|
4
|
11
|
11
|
8
|
8
|
|
4
|
11
|
12
|
10
|
12
|
11
|
5
|
6
|
4
|
6
|
0
|
4
|
0
|
10
|
Which is a code with the following weight distribution
1y14+1092x12y2+168x13y1+936x14