Code details
best found code with parameters
q=13 k=3 n=44
minimum distance = 39
this is new optimal code
the previous bounds were -1/39
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 9 orbits of sizes:
|
3
|
12
|
16
|
48
|
48
|
16
|
12
|
16
|
12
|
The solution of the corresponding linear system of equations was found after less than 10 seconds:
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
4
|
5
|
4
|
3
|
5
|
1
|
4
|
2
|
0
|
This produces the following generator matrix
|
0
|
0
|
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
|
0
|
0
|
0
|
0
|
12
|
9
|
3
|
6
|
12
|
12
|
12
|
12
|
9
|
9
|
9
|
9
|
3
|
3
|
3
|
3
|
6
|
6
|
6
|
6
|
2
|
2
|
2
|
2
|
5
|
5
|
5
|
5
|
11
|
11
|
11
|
11
|
8
|
8
|
8
|
8
|
|
12
|
9
|
3
|
6
|
12
|
9
|
3
|
6
|
0
|
0
|
0
|
0
|
12
|
9
|
3
|
6
|
12
|
9
|
3
|
6
|
12
|
9
|
3
|
6
|
12
|
9
|
3
|
6
|
1
|
4
|
10
|
7
|
1
|
4
|
10
|
7
|
1
|
4
|
10
|
7
|
1
|
4
|
10
|
7
|
Which is a code with the following weight distribution
1y44+720x39y5+372x40y4+576x41y3+192x42y2+192x43y1+144x44