Code details

best found code with parameters
q=3 k=8 n=225
minimum distance = 141

this is new code


the previous bounds were 138/146
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 1002 seconds:

0 0 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 56 56 57 56 81 83 65 65 84 81 83 65 74 75 66 83 74 74 81 84 65 83 65 81 75 65 83 74 81 75 74 83 74 63 75 83 74 65 81 75 74 74 83 63 75 83 74 74 63 66 74 83 74 81 66 74 74 83 81 84 83 65 65 81 84 74 74 74 63


This produces the following generator matrix

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 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 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 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 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 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 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 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 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
1y225+448x141y84+1344x142y83+504x144y81+672x150y75+2016x151y74+336x159y66+1008x160y65+224x162y63+2x168y57+6x169y56