Code details
best found code with parameters
q=16 k=3 n=18
minimum distance = 16
this is new optimal code
the previous bounds were -1/16
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 25 orbits of sizes:
|
3
|
18
|
9
|
3
|
9
|
9
|
9
|
9
|
3
|
9
|
9
|
9
|
9
|
3
|
9
|
9
|
9
|
9
|
18
|
18
|
18
|
18
|
18
|
18
|
18
|
The solution of the corresponding linear system of equations was found after less than 500 seconds:
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
2
|
2
|
0
|
0
|
0
|
2
|
0
|
0
|
2
|
2
|
0
|
2
|
0
|
2
|
2
|
2
|
2
|
2
|
0
|
2
|
0
|
2
|
0
|
0
|
This produces the following generator matrix
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
|
1
|
14
|
4
|
5
|
9
|
10
|
11
|
6
|
15
|
1
|
14
|
4
|
5
|
9
|
10
|
11
|
6
|
15
|
|
10
|
9
|
4
|
6
|
14
|
1
|
15
|
5
|
11
|
1
|
15
|
10
|
9
|
5
|
4
|
6
|
11
|
14
|
Which is a code with the following weight distribution
1y18+2295x16y2+1800x18