Code details
best found code with parameters
q=17 k=3 n=239
minimum distance = 224
this is new optimal code
the previous bounds were -1/224
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 51 orbits of sizes:
2
|
2
|
1
|
8
|
4
|
8
|
8
|
4
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
4
|
8
|
8
|
4
|
4
|
8
|
8
|
8
|
8
|
4
|
4
|
8
|
8
|
8
|
8
|
4
|
8
|
4
|
4
|
8
|
8
|
8
|
8
|
4
|
4
|
8
|
4
|
4
|
4
|
4
|
8
|
4
|
4
|
2
|
4
|
The solution of the corresponding linear system of equations was found after less than 8003 seconds:
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
14
|
15
|
14
|
14
|
13
|
14
|
14
|
0
|
14
|
14
|
14
|
14
|
14
|
14
|
15
|
14
|
15
|
14
|
15
|
13
|
13
|
14
|
14
|
14
|
15
|
15
|
15
|
14
|
14
|
15
|
15
|
13
|
14
|
13
|
15
|
14
|
14
|
14
|
15
|
15
|
13
|
15
|
13
|
15
|
15
|
14
|
14
|
14
|
14
|
15
|
14
|
This produces the following generator matrix
0
|
0
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
16
|
0
|
16
|
12
|
4
|
8
|
16
|
14
|
12
|
10
|
2
|
4
|
6
|
8
|
16
|
1
|
12
|
5
|
13
|
4
|
9
|
8
|
16
|
12
|
4
|
8
|
16
|
1
|
12
|
5
|
13
|
4
|
9
|
8
|
16
|
12
|
15
|
11
|
3
|
7
|
4
|
8
|
16
|
12
|
15
|
11
|
3
|
7
|
4
|
8
|
16
|
14
|
12
|
10
|
2
|
4
|
6
|
8
|
16
|
12
|
15
|
11
|
3
|
7
|
4
|
8
|
16
|
12
|
15
|
11
|
3
|
7
|
4
|
8
|
16
|
12
|
4
|
8
|
16
|
14
|
12
|
10
|
2
|
4
|
6
|
8
|
16
|
12
|
4
|
8
|
14
|
10
|
2
|
6
|
14
|
1
|
5
|
10
|
2
|
13
|
9
|
6
|
14
|
15
|
11
|
10
|
2
|
3
|
7
|
6
|
14
|
10
|
2
|
6
|
14
|
15
|
11
|
10
|
2
|
3
|
7
|
6
|
14
|
15
|
11
|
10
|
2
|
3
|
7
|
6
|
14
|
1
|
5
|
10
|
2
|
13
|
9
|
6
|
14
|
1
|
5
|
10
|
2
|
13
|
9
|
6
|
14
|
10
|
2
|
6
|
0
|
0
|
0
|
0
|
14
|
10
|
2
|
6
|
1
|
5
|
13
|
9
|
1
|
5
|
13
|
9
|
1
|
5
|
15
|
11
|
3
|
7
|
13
|
9
|
1
|
5
|
15
|
11
|
3
|
7
|
13
|
9
|
1
|
5
|
15
|
11
|
3
|
7
|
13
|
9
|
1
|
5
|
13
|
9
|
1
|
5
|
13
|
9
|
0
|
0
|
0
|
0
|
1
|
5
|
13
|
9
|
15
|
11
|
3
|
7
|
15
|
11
|
3
|
7
|
15
|
11
|
3
|
7
|
0
|
0
|
0
|
0
|
15
|
11
|
3
|
7
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
16
|
0
|
0
|
8
|
12
|
4
|
16
|
6
|
8
|
10
|
12
|
4
|
2
|
16
|
14
|
9
|
8
|
13
|
4
|
12
|
5
|
16
|
1
|
4
|
8
|
16
|
12
|
13
|
12
|
1
|
8
|
16
|
9
|
4
|
5
|
7
|
11
|
8
|
12
|
4
|
16
|
3
|
15
|
3
|
7
|
4
|
8
|
16
|
12
|
15
|
11
|
10
|
12
|
14
|
16
|
8
|
6
|
4
|
2
|
11
|
15
|
12
|
16
|
8
|
4
|
7
|
3
|
15
|
3
|
16
|
4
|
12
|
8
|
11
|
7
|
12
|
16
|
8
|
4
|
14
|
16
|
2
|
4
|
12
|
10
|
8
|
6
|
16
|
4
|
12
|
8
|
14
|
2
|
10
|
6
|
1
|
14
|
10
|
5
|
13
|
2
|
6
|
9
|
15
|
14
|
2
|
3
|
11
|
10
|
6
|
7
|
10
|
14
|
6
|
2
|
3
|
2
|
6
|
7
|
15
|
14
|
10
|
11
|
7
|
6
|
10
|
11
|
3
|
2
|
14
|
15
|
13
|
10
|
6
|
1
|
9
|
14
|
2
|
5
|
9
|
6
|
2
|
13
|
5
|
10
|
14
|
1
|
6
|
10
|
2
|
14
|
14
|
10
|
2
|
6
|
0
|
0
|
0
|
0
|
1
|
13
|
5
|
9
|
5
|
1
|
9
|
13
|
15
|
11
|
1
|
5
|
13
|
9
|
3
|
7
|
11
|
7
|
13
|
1
|
9
|
5
|
15
|
3
|
3
|
15
|
5
|
9
|
1
|
13
|
7
|
11
|
13
|
9
|
1
|
5
|
9
|
5
|
13
|
1
|
1
|
5
|
13
|
9
|
0
|
0
|
0
|
0
|
11
|
15
|
7
|
3
|
3
|
7
|
15
|
11
|
7
|
11
|
3
|
15
|
15
|
11
|
3
|
7
|
0
|
0
|
0
|
0
|
14
|
10
|
2
|
6
|
1
|
15
|
7
|
9
|
5
|
11
|
3
|
13
|
Which is a code with the following weight distribution
1y239+1408x224y15+2992x225y14+448x226y13+64x239