Code details
best found code with parameters
q=16 k=3 n=142
minimum distance = 132
this is new optimal code
the previous bounds were -1/132
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 37 orbits of sizes:
|
2
|
10
|
5
|
1
|
10
|
5
|
10
|
10
|
10
|
5
|
10
|
10
|
10
|
5
|
10
|
5
|
5
|
5
|
10
|
10
|
10
|
10
|
10
|
5
|
10
|
10
|
5
|
5
|
10
|
5
|
5
|
10
|
10
|
5
|
5
|
5
|
5
|
The solution of the corresponding linear system of equations was found after less than 500 seconds:
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
6
|
8
|
10
|
2
|
10
|
8
|
9
|
10
|
9
|
10
|
9
|
9
|
9
|
8
|
9
|
8
|
8
|
8
|
0
|
10
|
10
|
9
|
10
|
10
|
10
|
10
|
10
|
10
|
9
|
10
|
6
|
10
|
10
|
8
|
8
|
8
|
10
|
This produces the following generator matrix
|
0
|
0
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
15
|
|
0
|
15
|
0
|
0
|
0
|
0
|
0
|
1
|
4
|
7
|
13
|
10
|
8
|
14
|
5
|
9
|
2
|
3
|
11
|
6
|
12
|
15
|
8
|
14
|
5
|
9
|
2
|
3
|
11
|
6
|
12
|
15
|
1
|
4
|
7
|
9
|
13
|
10
|
3
|
6
|
12
|
15
|
9
|
3
|
6
|
12
|
15
|
9
|
3
|
6
|
12
|
15
|
9
|
3
|
6
|
12
|
15
|
1
|
4
|
7
|
9
|
13
|
10
|
3
|
6
|
12
|
15
|
8
|
14
|
5
|
9
|
2
|
3
|
11
|
6
|
12
|
15
|
8
|
14
|
5
|
9
|
2
|
3
|
11
|
6
|
12
|
15
|
8
|
14
|
5
|
2
|
11
|
8
|
14
|
5
|
2
|
11
|
1
|
8
|
14
|
4
|
5
|
7
|
2
|
13
|
10
|
11
|
8
|
14
|
5
|
2
|
11
|
1
|
8
|
14
|
4
|
5
|
7
|
2
|
13
|
10
|
11
|
1
|
4
|
7
|
13
|
10
|
1
|
4
|
7
|
13
|
10
|
1
|
4
|
7
|
13
|
10
|
1
|
4
|
7
|
13
|
10
|
|
15
|
0
|
1
|
4
|
7
|
13
|
10
|
0
|
0
|
0
|
0
|
0
|
12
|
6
|
15
|
11
|
3
|
2
|
9
|
14
|
8
|
5
|
9
|
3
|
12
|
8
|
15
|
14
|
6
|
11
|
5
|
2
|
12
|
9
|
6
|
4
|
15
|
3
|
10
|
7
|
1
|
13
|
12
|
3
|
15
|
9
|
6
|
3
|
9
|
6
|
15
|
12
|
6
|
12
|
9
|
3
|
15
|
3
|
15
|
12
|
10
|
6
|
9
|
1
|
13
|
7
|
4
|
6
|
15
|
9
|
5
|
12
|
11
|
3
|
8
|
2
|
14
|
15
|
9
|
3
|
14
|
6
|
5
|
12
|
2
|
11
|
8
|
5
|
14
|
8
|
11
|
2
|
8
|
2
|
11
|
14
|
5
|
14
|
7
|
1
|
11
|
10
|
8
|
13
|
2
|
5
|
4
|
11
|
5
|
14
|
2
|
8
|
11
|
4
|
13
|
8
|
7
|
5
|
10
|
14
|
2
|
1
|
4
|
1
|
13
|
7
|
10
|
7
|
4
|
1
|
10
|
13
|
1
|
13
|
10
|
4
|
7
|
13
|
10
|
7
|
1
|
4
|
Which is a code with the following weight distribution
1y142+1875x132y10+1200x133y9+750x134y8+105x136y6+15x140y2+150x142