Code details

best found code with parameters
q=3 k=7 n=60
minimum distance = 36

this is new optimal code


the previous bounds were 34/36
this is a projective code


We used the prescribed group of automorphisms with the following generators


0 0 2 0 0 0 0
2 0 0 0 0 0 0
0 2 0 0 0 0 0
0 0 0 0 0 2 0
0 0 0 2 0 0 0
0 0 0 0 2 0 0
0 0 0 0 0 0 2

1 0 0 0 0 0 0
0 2 0 0 0 0 0
0 0 2 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 2 0
0 0 0 0 0 0 2

This group make 67 orbits of sizes:

1 3 6 6 12 4 4 4 3 6 6 12 6 12 12 24 6 12 12 24 12 24 24 24 24 6 12 12 24 12 12 12 24 24 24 12 24 12 24 12 24 24 24 24 24 24 24 24 24 24 4 8 24 24 24 24 24 24 8 8 8 24 24 24 24 24 24


The solution of the corresponding linear system of equations was found after less than 22 seconds:

0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 0 0 24 18 9 24 24 24 15 15 18 21 24 18 24 18 24 18 24 18 24 18 24 18 18 21 21 24 12 24 21 24 21 21 18 24 15 24 21 18 24 18 15 18 15 24 15 21 21 24 21 21 24 24 18 18 18 24 24 24 15 15 15 15 24 24 24 15 15


This produces the following generator matrix

0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
0 0 0 0 0 0 0 0 2 2 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1
0 0 0 0 0 0 2 2 0 0 0 0 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1
0 0 0 0 2 2 0 0 0 0 0 0 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 0 0 2 2 1 1 0 0 2 2 1 1 0 0 2 2 1 1 0 0 2 2 1 1
0 0 2 2 0 0 0 0 0 0 0 0 2 2 1 1 1 1 2 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 0 1 0 2 2 1 0 2 0 1 2 1 0 2 0 1 2 1 0 1 0 2
2 2 0 0 0 0 0 0 0 0 0 0 2 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 2 2 1 1 1 1 2 2 1 2 1 0 2 0 2 1 1 0 2 0 1 2 2 0 1 0 2 1 2 0 1 0
2 1 2 1 2 1 2 1 2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 1 1 2 1 2 1 2 2 1 2 1 2 1 1 2 2 1 1 2 2 1



Which is a code with the following weight distribution
1y60+742x36y24+444x39y21+564x42y18+400x45y15+24x48y12+12x51y9