Code details

best found code with parameters
q=3 k=8 n=224
minimum distance = 141

this is new code


the previous bounds were 138/145
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:

0 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 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 56 56 56 56 80 65 65 83 83 80 65 74 74 83 74 65 83 74 80 65 83 65 83 80 74 74 65 83 80 74 74 74 83 62 65 74 83 74 80 83 74 74 74 62 74 74 83 74 62 74 65 74 83 80 83 65 74 74 80 65 83 83 65 80 74 83 74 74 62


This produces the following generator matrix

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
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 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 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 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
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 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 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 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 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 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



Which is a code with the following weight distribution
1y224+1792x141y83+504x144y80+2688x150y74+1344x159y65+224x162y62+8x168y56