Code details

best found code with parameters
q=3 k=6 n=202
minimum distance = 132

this is new code


the previous bounds were 131/133
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

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

This group make 20 orbits of sizes:

6 15 10 15 6 1 6 15 30 10 30 30 30 30 30 15 30 30 15 10


The solution of the corresponding linear system of equations was found after less than 10 seconds:

0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 61 67 49 67 70 31 70 67 70 67 70 61 67 70 67 70 70 67 70 67


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y202+324x132y70+310x135y67+72x141y61+20x153y49+2x171y31