Code details
best found code with parameters
q=13 k=3 n=23
minimum distance = 20
this is new optimal code
the previous bounds were -1/20
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 51 orbits of sizes:
|
1
|
1
|
4
|
1
|
4
|
2
|
4
|
4
|
4
|
4
|
4
|
4
|
4
|
4
|
4
|
4
|
4
|
4
|
2
|
4
|
4
|
4
|
4
|
4
|
4
|
2
|
4
|
4
|
4
|
4
|
4
|
4
|
2
|
4
|
4
|
4
|
4
|
4
|
4
|
2
|
4
|
4
|
4
|
4
|
4
|
4
|
2
|
4
|
4
|
4
|
4
|
The solution of the corresponding linear system of equations was found after less than 10 seconds:
|
1
|
1
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
2
|
2
|
2
|
2
|
3
|
3
|
0
|
0
|
0
|
3
|
3
|
3
|
1
|
3
|
3
|
2
|
0
|
0
|
3
|
3
|
2
|
0
|
3
|
0
|
1
|
3
|
2
|
1
|
2
|
0
|
1
|
3
|
3
|
1
|
1
|
3
|
0
|
2
|
2
|
3
|
3
|
0
|
3
|
2
|
2
|
0
|
1
|
3
|
2
|
3
|
3
|
This produces the following generator matrix
|
0
|
0
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
|
0
|
12
|
0
|
12
|
12
|
6
|
6
|
4
|
4
|
10
|
10
|
2
|
2
|
8
|
8
|
9
|
9
|
3
|
3
|
5
|
5
|
11
|
11
|
|
12
|
0
|
0
|
5
|
11
|
2
|
8
|
2
|
8
|
5
|
11
|
1
|
7
|
4
|
10
|
12
|
6
|
9
|
3
|
12
|
6
|
9
|
3
|
Which is a code with the following weight distribution
1y23+840x20y3+516x21y2+312x22y1+528x23