Code details

best found code with parameters
q=3 k=8 n=205
minimum distance = 128

this is new code


the previous bounds were 126/133
this is a projective code


We used the prescribed group of automorphisms with the following generators


0 0 1 1 1 1 0 0
1 0 1 1 0 0 0 0
1 1 1 1 0 1 0 1
0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0
0 0 1 0 0 1 0 1
1 0 0 1 1 0 0 1
0 0 1 0 1 0 1 1

This group make 80 orbits of sizes:

41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41


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

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 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 74 77 76 57 73 69 70 76 77 60 72 77 66 72 66 67 67 60 73 58 76 58 66 60 69 65 73 72 72 68 74 60 77 70 68 74 68 57 69 53 60 68 68 68 58 65 73 74 67 76 73 58 73 72 66 72 77 77 76 77 53 70 68 65 60 60 68 57 57 73 76 60 73 77 72 67 68 65 70 72


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y205+656x128y77+492x129y76+328x131y74+656x132y73+656x133y72+328x135y70+246x136y69+738x137y68+328x138y67+328x139y66+328x140y65+656x145y60+328x147y58+328x148y57+164x152y53