Code details

best found code with parameters
q=3 k=7 n=222
minimum distance = 144

this is new code


the previous bounds were 143/145
this is a projective code


We used the prescribed group of automorphisms with the following generators


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

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

This group make 45 orbits of sizes:

26 26 26 13 26 26 26 26 26 26 26 26 13 26 26 26 26 26 26 26 26 26 26 26 26 26 26 1 26 26 26 26 26 26 26 26 26 26 26 13 26 26 26 26 13


The solution of the corresponding linear system of equations was found after less than 1534 seconds:

0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 78 69 78 78 69 78 60 78 60 78 60 78 78 78 69 78 69 60 78 78 78 78 78 78 69 78 78 78 78 78 78 78 78 78 69 69 78 69 78 78 69 69 78 60 78


This produces the following generator matrix

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



Which is a code with the following weight distribution
1y222+1458x144y78+468x153y69+260x162y60