Code details

best found code with parameters
q=3 k=8 n=226
minimum distance = 142

this is new code


the previous bounds were 139/147
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:

0 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 56 57 56 82 84 65 65 84 82 84 65 74 75 66 83 74 75 82 84 65 83 66 82 75 65 83 75 82 75 74 83 75 64 75 83 74 66 82 75 74 74 84 64 75 83 74 75 64 66 74 83 75 82 66 74 74 84 82 84 83 65 66 82 84 74 74 75 64


This produces the following generator matrix

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 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 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 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 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 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
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
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
1y226+896x142y84+896x143y83+504x144y82+1344x151y75+1344x152y74+672x160y66+672x161y65+224x162y64+4x169y57+4x170y56