Code details

best found code with parameters
q=3 k=6 n=217
minimum distance = 142

this is new code


the previous bounds were 141/143
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

This group make 24 orbits of sizes:

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


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

1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 48 73 75 66 66 73 75 75 73 75 73 75 75 73 75 73 75 66 73 75 55 48 48 73


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y217+336x142y75+234x144y73+144x151y66+8x162y55+6x169y48