Code details

best found code with parameters
q=3 k=8 n=228
minimum distance = 144

this is new code


the previous bounds were 141/148
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

This group make 69 orbits of sizes:

1 1 1 1 28 56 56 56 56 28 56 56 56 56 28 56 56 56 56 56 56 56 56 28 56 56 56 56 28 56 56 56 56 28 56 56 56 56 28 56 56 56 56 28 56 56 56 56 28 56 56 56 56 28 56 56 56 56 28 56 56 56 56 28 56 56 56 56 28


The solution of the corresponding linear system of equations was found after less than 766 seconds:

1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 57 57 57 57 84 66 66 84 84 84 66 75 84 75 66 75 84 75 84 84 66 66 84 84 75 75 66 84 84 75 75 75 84 66 75 66 84 75 84 75 84 75 75 66 75 75 84 75 66 66 75 75 84 84 66 84 75 75 84 84 66 84 66 84 84 75 75 75 66


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y228+2296x144y84+2688x153y75+1568x162y66+8x171y57