Code details
best found code with parameters
q=11 k=3 n=67
minimum distance = 60
this is new optimal code
the previous bounds were -1/60
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 13 orbits of sizes:
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11
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11
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11
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11
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11
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11
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11
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11
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11
|
11
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11
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11
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1
|
The solution of the corresponding linear system of equations was found after less than 10 seconds:
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1
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0
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1
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1
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0
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0
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1
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1
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0
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0
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1
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0
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1
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7
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1
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7
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7
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6
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6
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6
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7
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6
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7
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6
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7
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1
|
This produces the following generator matrix
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0
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0
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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0
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0
|
10
|
10
|
10
|
10
|
10
|
10
|
10
|
10
|
10
|
0
|
0
|
10
|
10
|
10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
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10
|
10
|
10
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0
|
10
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10
|
10
|
10
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10
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10
|
10
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10
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10
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10
|
10
|
|
0
|
10
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0
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10
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8
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2
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4
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9
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7
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6
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5
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1
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2
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2
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7
|
7
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3
|
3
|
6
|
6
|
5
|
5
|
10
|
10
|
1
|
8
|
8
|
4
|
4
|
9
|
9
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6
|
5
|
10
|
10
|
1
|
4
|
4
|
3
|
3
|
6
|
6
|
5
|
5
|
0
|
0
|
10
|
10
|
1
|
8
|
8
|
9
|
9
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3
|
3
|
10
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0
|
0
|
10
|
10
|
1
|
2
|
2
|
4
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7
|
7
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1
|
|
10
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5
|
10
|
6
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4
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4
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1
|
3
|
9
|
3
|
9
|
5
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0
|
10
|
1
|
4
|
10
|
3
|
1
|
6
|
4
|
3
|
10
|
6
|
9
|
9
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3
|
4
|
7
|
2
|
7
|
2
|
6
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0
|
3
|
7
|
3
|
5
|
2
|
4
|
0
|
9
|
10
|
1
|
2
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5
|
1
|
5
|
10
|
10
|
7
|
0
|
1
|
0
|
6
|
7
|
0
|
7
|
2
|
9
|
2
|
6
|
5
|
0
|
7
|
5
|
6
|
Which is a code with the following weight distribution
1y67+660x60y7+550x61y6+120x66y1