Code details

best found code with parameters
q=3 k=8 n=227
minimum distance = 143

this is new code


the previous bounds were 140/147
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 1000 seconds:

1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 57 57 57 56 83 84 66 65 84 83 84 66 74 75 66 83 75 75 83 84 65 84 66 83 75 65 84 75 83 75 74 84 75 65 75 83 75 66 83 75 74 75 84 65 75 83 75 75 65 66 74 84 75 83 66 74 75 84 83 84 83 66 66 83 84 74 75 75 65


This produces the following generator matrix

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 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 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 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 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 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 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 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 0 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 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 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 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



Which is a code with the following weight distribution
1y227+1344x143y84+952x144y83+2016x152y75+672x153y74+1008x161y66+560x162y65+6x170y57+2x171y56