Code details
best found code with parameters
q=17 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 21 orbits of sizes:
|
3
|
12
|
12
|
24
|
24
|
24
|
12
|
24
|
24
|
12
|
24
|
24
|
12
|
12
|
12
|
12
|
12
|
4
|
12
|
6
|
6
|
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
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
1
|
2
|
0
|
0
|
0
|
2
|
2
|
2
|
0
|
2
|
1
|
0
|
0
|
2
|
0
|
2
|
0
|
2
|
2
|
2
|
1
|
0
|
This produces the following generator matrix
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
0
|
0
|
16
|
16
|
16
|
16
|
|
12
|
12
|
15
|
15
|
10
|
10
|
2
|
2
|
7
|
7
|
4
|
4
|
16
|
16
|
0
|
0
|
11
|
3
|
|
12
|
4
|
10
|
2
|
15
|
7
|
15
|
7
|
10
|
2
|
12
|
4
|
12
|
4
|
11
|
3
|
0
|
0
|
Which is a code with the following weight distribution
1y18+2448x16y2+288x17y1+2176x18