Code details

best found code with parameters
q=3 k=6 n=219
minimum distance = 144

this is new optimal code


the previous bounds were 143/144
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 2 0 0 0
0 0 0 2 0 0
0 0 0 0 2 0
0 0 0 0 0 2

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

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

This group make 20 orbits of sizes:

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


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

0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 1 0 75 75 66 75 66 75 66 75 75 75 75 75 75 57 75 75 75 57 75 48


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y219+568x144y75+144x153y66+14x162y57+2x171y48