Code details
best found code with parameters
q=13 k=3 n=79
minimum distance = 72
this is new optimal code
the previous bounds were -1/72
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 15 orbits of sizes:
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13
|
13
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13
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13
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13
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13
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13
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13
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13
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13
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13
|
13
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13
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13
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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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0
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0
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0
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0
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0
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0
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0
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0
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1
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1
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1
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1
|
1
|
1
|
1
|
1
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7
|
7
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6
|
7
|
7
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6
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6
|
6
|
6
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7
|
7
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6
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7
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0
|
This produces the following generator matrix
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12
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12
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12
|
12
|
12
|
12
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12
|
12
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12
|
12
|
12
|
12
|
12
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0
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
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0
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0
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
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0
|
0
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
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0
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0
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
12
|
|
0
|
4
|
4
|
2
|
2
|
9
|
9
|
3
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3
|
10
|
10
|
7
|
7
|
12
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0
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12
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1
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1
|
2
|
2
|
9
|
9
|
10
|
10
|
7
|
7
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0
|
1
|
1
|
4
|
9
|
9
|
5
|
5
|
3
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8
|
8
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7
|
7
|
12
|
12
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0
|
12
|
12
|
1
|
1
|
4
|
4
|
9
|
3
|
3
|
7
|
12
|
12
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0
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12
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12
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2
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2
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5
|
5
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8
|
8
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10
|
10
|
12
|
12
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0
|
12
|
12
|
4
|
4
|
5
|
5
|
3
|
3
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8
|
8
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0
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|
4
|
5
|
6
|
2
|
5
|
2
|
7
|
11
|
10
|
4
|
7
|
11
|
6
|
7
|
3
|
1
|
5
|
11
|
11
|
7
|
5
|
3
|
1
|
9
|
9
|
7
|
11
|
9
|
3
|
3
|
10
|
6
|
9
|
11
|
8
|
8
|
6
|
2
|
10
|
4
|
8
|
1
|
2
|
10
|
4
|
10
|
9
|
11
|
9
|
4
|
2
|
1
|
9
|
10
|
8
|
4
|
3
|
3
|
8
|
10
|
7
|
4
|
7
|
5
|
10
|
2
|
11
|
2
|
5
|
8
|
1
|
8
|
5
|
6
|
1
|
6
|
2
|
3
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0
|
Which is a code with the following weight distribution
1y79+1092x72y7+936x73y6+12x78y1+156x79