Code details
best found code with parameters
q=23 k=3 n=34
minimum distance = 31
this is new optimal code
the previous bounds were -1/31
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 33 orbits of sizes:
|
3
|
6
|
4
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
24
|
24
|
24
|
24
|
24
|
24
|
24
|
24
|
12
|
24
|
24
|
24
|
24
|
12
|
24
|
24
|
24
|
12
|
12
|
12
|
The solution of the corresponding linear system of equations was found after less than 100 seconds:
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
2
|
3
|
3
|
2
|
3
|
1
|
1
|
3
|
3
|
3
|
3
|
3
|
1
|
3
|
2
|
2
|
0
|
0
|
1
|
2
|
0
|
2
|
1
|
0
|
0
|
2
|
2
|
3
|
2
|
0
|
2
|
0
|
0
|
This produces the following generator matrix
|
0
|
0
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
22
|
|
22
|
22
|
0
|
0
|
22
|
11
|
22
|
22
|
11
|
11
|
2
|
2
|
16
|
16
|
4
|
4
|
18
|
18
|
6
|
6
|
9
|
9
|
20
|
20
|
17
|
17
|
7
|
7
|
15
|
15
|
5
|
5
|
13
|
13
|
|
22
|
11
|
22
|
11
|
0
|
0
|
22
|
11
|
22
|
11
|
6
|
17
|
18
|
7
|
9
|
20
|
16
|
5
|
2
|
13
|
4
|
15
|
4
|
15
|
2
|
13
|
16
|
5
|
9
|
20
|
18
|
7
|
6
|
17
|
Which is a code with the following weight distribution
1y34+2860x31y3+3762x32y2+1848x33y1+3696x34