Code details

best found code with parameters
q=3 k=8 n=200
minimum distance = 126

this is new code


the previous bounds were 124/129
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

This group make 82 orbits of sizes:

40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40


The solution of the corresponding linear system of equations was found after less than 95 seconds:

0 0 0 0 0 0 0 1 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 0 0 0 1 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 65 65 74 65 74 65 65 74 74 56 65 65 74 74 47 65 74 65 56 74 65 56 74 74 65 56 74 74 56 65 65 56 74 65 74 74 65 65 65 65 65 65 74 56 65 74 74 56 65 65 65 74 74 56 65 65 74 65 65 65 65 65 74 65 74 65 74 65 65 65 74 74 74 65 65 56 65 74 74 56 65 56


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y200+2320x126y74+3200x135y65+960x144y56+80x153y47