Code details

best found code with parameters
q=3 k=6 n=201
minimum distance = 131

this is new code


the previous bounds were 130/132
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 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 61 67 48 67 70 30 70 67 69 66 70 61 67 69 67 69 70 67 69 66


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 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 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 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 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 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 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
1y201+144x131y70+180x132y69+270x134y67+40x135y66+72x140y61+20x153y48+2x171y30