Code details

best found code with parameters
q=3 k=6 n=191
minimum distance = 126

this is new optimal code


the previous bounds were 125/126
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

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

This group make 20 orbits of sizes:

6 15 10 15 6 1 6 15 30 10 30 30 30 30 30 15 30 30 15 10


The solution of the corresponding linear system of equations was found after less than 10 seconds:

1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 65 65 47 65 56 20 65 65 65 65 56 65 65 65 65 65 65 65 65 65


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y191+634x126y65+72x135y56+20x144y47+2x171y20