Code details

best found code with parameters
q=3 k=7 n=202
minimum distance = 129

this is new code


the previous bounds were 128/132
this is not a projective code, the bound was 3


We used the prescribed group of automorphisms with the following generators


2 0 2 2 0 0 0
0 2 0 0 0 0 2
0 0 0 0 0 2 0
2 0 0 2 0 0 0
0 0 0 0 0 0 2
2 0 0 0 0 0 0
2 0 0 0 2 2 2

This group make 35 orbits of sizes:

8 4 40 40 40 40 40 20 40 20 40 40 40 40 40 40 40 40 40 10 10 40 10 40 40 20 40 40 40 40 40 10 40 20 1


The solution of the corresponding linear system of equations was found after less than 94 seconds:

0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 64 73 73 64 70 73 64 73 73 55 70 70 73 55 73 58 61 55 70 64 70 73 70 70 64 70 64 70 70 73 70 58 70 52 40


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y202+720x129y73+596x132y70+480x138y64+80x141y61+60x144y58+240x147y55+8x150y52+2x162y40