Code details
best found code with parameters
q=16 k=3 n=120
minimum distance = 112
this is new optimal code
the previous bounds were -1/112
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 29 orbits of sizes:
|
6
|
6
|
6
|
6
|
6
|
1
|
6
|
6
|
6
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
4
|
4
|
The solution of the corresponding linear system of equations was found after less than 500 seconds:
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
0
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
0
|
8
|
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
|
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
|
|
1
|
1
|
14
|
14
|
15
|
15
|
4
|
4
|
11
|
11
|
15
|
15
|
2
|
2
|
13
|
13
|
15
|
15
|
8
|
8
|
7
|
7
|
15
|
15
|
1
|
14
|
4
|
5
|
9
|
9
|
10
|
3
|
11
|
6
|
6
|
12
|
1
|
14
|
4
|
5
|
9
|
9
|
10
|
3
|
11
|
6
|
6
|
12
|
8
|
5
|
7
|
9
|
2
|
13
|
10
|
3
|
3
|
6
|
12
|
12
|
8
|
5
|
7
|
9
|
2
|
13
|
10
|
3
|
3
|
6
|
12
|
12
|
1
|
14
|
4
|
5
|
2
|
2
|
13
|
13
|
10
|
3
|
11
|
12
|
1
|
8
|
8
|
14
|
4
|
5
|
7
|
7
|
10
|
3
|
11
|
12
|
8
|
4
|
4
|
5
|
7
|
9
|
2
|
13
|
10
|
11
|
11
|
6
|
1
|
1
|
8
|
14
|
14
|
5
|
7
|
9
|
2
|
13
|
10
|
6
|
|
1
|
15
|
14
|
15
|
1
|
14
|
4
|
15
|
11
|
15
|
4
|
11
|
2
|
15
|
13
|
15
|
2
|
13
|
8
|
15
|
7
|
15
|
8
|
7
|
4
|
9
|
10
|
9
|
3
|
6
|
1
|
14
|
12
|
5
|
11
|
6
|
10
|
3
|
1
|
6
|
14
|
5
|
4
|
9
|
6
|
9
|
12
|
11
|
2
|
8
|
12
|
7
|
5
|
6
|
12
|
13
|
10
|
3
|
9
|
3
|
5
|
2
|
9
|
12
|
8
|
3
|
3
|
6
|
12
|
13
|
7
|
10
|
5
|
2
|
14
|
3
|
4
|
13
|
10
|
12
|
11
|
1
|
13
|
2
|
11
|
1
|
7
|
7
|
5
|
12
|
10
|
3
|
14
|
8
|
8
|
4
|
4
|
9
|
13
|
11
|
5
|
11
|
6
|
8
|
2
|
4
|
7
|
10
|
7
|
6
|
9
|
1
|
13
|
14
|
2
|
10
|
1
|
5
|
8
|
14
|
Which is a code with the following weight distribution
1y120+3825x112y8+270x120